Re: The benefit of a symbol for 2 pi
One of the new characters scheduled for Unicode 3.2 is U+213F DOUBLE-STRUCK CAPITAL PI (A 500-byte GIF is attached.) Double-struck pi! What better symbol to represent 2 * pi? -Doug Ewell Fullerton, California
Re: The benefit of a symbol for 2 pi
At 07:40 PM 1/26/02 -0500, [EMAIL PROTECTED] wrote: One of the new characters scheduled for Unicode 3.2 is U+213F DOUBLE-STRUCK CAPITAL PI (A 500-byte GIF is attached.) Double-struck pi! What better symbol to represent 2 * pi? These double struck symbols are used by mathematical sofware precisely because they are NOT yet used for regular operators or variables. Please don't make such recommendations before understanding the nature of the symbol you are suggesting to abuse! A./
Re: The benefit of a symbol for 2 pi
In a message dated 2002-01-26 19:58:28 Pacific Standard Time, [EMAIL PROTECTED] writes: Double-struck pi! What better symbol to represent 2 * pi? These double struck symbols are used by mathematical sofware precisely because they are NOT yet used for regular operators or variables. Please don't make such recommendations before understanding the nature of the symbol you are suggesting to abuse! Sorry. I probably should have guessed that they were being added to 3.2, to the BMP no less, for a specific reason. -Doug Ewell Fullerton, California
RE: The benefit of a symbol for 2 pi
On Sat, 19 Jan 2002, Murray Sargent wrote: Capital pi is to product as capital sigma is to summation. But if I'm not mistaken, Unicode already has a separate character for n-ary products and summation (U+220F, U+2211), distinct from the capital Greek letters *and* the variant forms in the mathematical alphanumeric block. If capital pi is the way to go, why not use U+1D6F1 MATHEMATICAL ITALIC CAPITAL PI or U+1D72B MATHEMATICAL BOLD ITALIC CAPITAL PI, for instance? Sampo Syreeni, aka decoy - mailto:[EMAIL PROTECTED], tel:+358-50-5756111 student/math+cs/helsinki university, http://www.iki.fi/~decoy/front openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
RE: The benefit of a symbol for 2 pi
Capital pi is to product as capital sigma is to summation. -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] Sent: Sun 2002/01/20 02:19 To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Re: The benefit of a symbol for 2 pi In a message dated 2002-01-19 17:07:34 Pacific Standard Time, [EMAIL PROTECTED] writes: In fact Cajori mentions that the capital pi Was used at some point for 6.28... so someone had the same idea long before I did. That is a VERY intriguing thought, one that should be especially worthy of mention to the AMS. I thought capital pi already had an established meaning, but perhaps that is in physics or some other branch of science rather than mathematics. -Doug Ewell Fullerton, California
Re: The benefit of a symbol for 2 pi
Hi James, I appreciate the research, and the humor! 2 pis = peace, eh? (not on the unicode list! :-) but I like that especially since the issue of a name has been problematic. e to the i peace =1 circumference = peace times r, integral from zero to peace, period = peace over frequency, has a nice ring to it! Peace, Bob On Sat, 19 Jan 2002, James Kass wrote: Couldn't find such a glyph, but there are some that are vaguely similar: U+29B7 CIRCLED PARALLEL U+238B BROKEN CIRCLE WITH NORTHWEST ARROW U+229D CIRCLED DASH And, with a note of mild humor, possibly the PEACE SIGN at U+262E might serve? It doesn't seem to be used much these days. With the vagaries of English plurals, perhaps peace is the proper plural for pi... Best regards, James Kass, P.S. - With so-called smart fonts, which are really just OpenType fonts, a string such as the digit two followed by the Greek pi could be replaced in the display with a special glyph for 2pi or newpi. This would not alter the original file, it only impacts the display. The procedure is called glyph substitution and support for OpenType is growing.
Re: The benefit of a symbol for 2 pi
In a message dated 2002-01-19 9:33:46 Pacific Standard Time, [EMAIL PROTECTED] writes: Has there been any consideration of practical alternatives, such as selecting a lookalike or similar character from the plethora of those already encoded and promoting its use to represent the newpi character? My own proposal was a pictogram: A circle with a radius to 3 o'clock, i.e. from 0 to 1 in the complex number plane. Pacman with mouth closed. Does that already exist in Unicode? :-) My dad's version is a lot more palatable for most people. A large number of glyphic variations of Latin and Greek letters were just added to Unicode 3.1 with the sole purpose of serving as mathematical identifiers. Apparently it was stressed by the AMS and others that these variations (bold, italic, double-struck, sans serif, etc.) are all significant and distinct in math notation. Could one of these characters, already approved and part of Unicode, be adopted to represent 2pi? In particular, consider the following already-encoded variants of pi: U+1D6B7 MATHEMATICAL BOLD CAPITAL PI U+1D6D1 MATHEMATICAL BOLD SMALL PI U+1D6E1 MATHEMATICAL BOLD PI SYMBOL U+1D6F1 MATHEMATICAL ITALIC CAPITAL PI U+1D70B MATHEMATICAL ITALIC SMALL PI U+1D71B MATHEMATICAL ITALIC PI SYMBOL U+1D72B MATHEMATICAL BOLD ITALIC CAPITAL PI U+1D745 MATHEMATICAL BOLD ITALIC SMALL PI U+1D755 MATHEMATICAL BOLD ITALIC PI SYMBOL U+1D765 MATHEMATICAL SANS-SERIF BOLD CAPITAL PI U+1D77F MATHEMATICAL SANS-SERIF BOLD SMALL PI U+1D78F MATHEMATICAL SANS-SERIF BOLD PI SYMBOL U+1D79F MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PI U+1D7B9 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PI U+1D7C9 MATHEMATICAL SANS-SERIF BOLD ITALIC PI SYMBOL Now, it may well be that a typographical variant of pi is not the best choice to represent (2 * pi). That's OK, there are still hundreds more of these math-specific characters to choose from. -Doug Ewell Fullerton, California
Re: The benefit of a symbol for 2 pi
At 13:32 -0500 2002-01-19, [EMAIL PROTECTED] wrote: In a message dated 2002-01-19 9:33:46 Pacific Standard Time, [EMAIL PROTECTED] writes: Has there been any consideration of practical alternatives, such as selecting a lookalike or similar character from the plethora of those already encoded and promoting its use to represent the newpi character? My own proposal was a pictogram: A circle with a radius to 3 o'clock, i.e. from 0 to 1 in the complex number plane. Pacman with mouth closed. Does that already exist in Unicode? :-) My dad's version is a lot more palatable for most people. A large number of glyphic variations of Latin and Greek letters were just added to Unicode 3.1 with the sole purpose of serving as mathematical identifiers. Apparently it was stressed by the AMS and others that these variations (bold, italic, double-struck, sans serif, etc.) are all significant and distinct in math notation. Could one of these characters, already approved and part of Unicode, be adopted to represent 2pi? That's up the the AMS, not to us. -- Michael Everson *** Everson Typography *** http://www.evertype.com
Re: The benefit of a symbol for 2 pi
In a message dated 2002-01-19 11:35:57 Pacific Standard Time, [EMAIL PROTECTED] writes: Could one of these characters, already approved and part of Unicode, be adopted to represent 2pi? That's up the the AMS, not to us. Indeed. It might be a good topic for the AMS discussion forum that Robert mentioned. -Doug Ewell Fullerton, California
Re: The benefit of a symbol for 2 pi
Robert Palais wrote, My own proposal was a pictogram: A circle with a radius to 3 o'clock, i.e. from 0 to 1 in the complex number plane. Pacman with mouth closed. Does that already exist in Unicode? :-) My dad's version is a lot more palatable for most people. Couldn't find such a glyph, but there are some that are vaguely similar: U+29B7 CIRCLED PARALLEL U+238B BROKEN CIRCLE WITH NORTHWEST ARROW U+229D CIRCLED DASH And, with a note of mild humor, possibly the PEACE SIGN at U+262E might serve? It doesn't seem to be used much these days. With the vagaries of English plurals, perhaps peace is the proper plural for pi... Best regards, James Kass, P.S. - With so-called smart fonts, which are really just OpenType fonts, a string such as the digit two followed by the Greek pi could be replaced in the display with a special glyph for 2pi or newpi. This would not alter the original file, it only impacts the display. The procedure is called glyph substitution and support for OpenType is growing.
Re: The benefit of a symbol for 2 pi
Robert Palais wrote: I will be doing so, and apologize if my inquiry intruded on your work, and at the same time, appreciate the many thoughtful considerations on the matter of process of symbol standardization that I received. and later: I apologize again if my misunderstanding that I was advised to bring it up directly here offended you... Please be assured that nobody here feels offended, intruded upon, or otherwise discommoded as a result of any of your inquiries. You have every right, and in fact you are strongly encouraged, to discuss your proposed new character and ask questions about adding it to Unicode. For my part at least, I feel it is important to explain to proponents WHY their proposed characters may not be suitable for encoding, rather than simply telling them No. Observing your discussions, I do wonder if the participants recognize the responsibility of their influence upon ideas, through symbols I think the Unicode Consortium and WG2 do understand this, and that is why they are so reluctant to encode symbols that do not have established usage, as in the case of 2 pi, or seek to make a social or political statement that the Consortium and WG2 do not intend, as in the case of copyleft. (but it seems some may enjoy it too much.) I am totally mystified by this remark. -Doug Ewell Fullerton, California
Re: The benefit of a symbol for 2 pi
On Fri, 18 Jan 2002 [EMAIL PROTECTED] wrote: For my part at least, I feel it is important to explain to proponents WHY their proposed characters may not be suitable for encoding, rather than simply telling them No. I thought that had been done quite well. I think the Unicode Consortium and WG2 do understand this, and that is why they are so reluctant to encode symbols that do not have established usage, as in the case of 2 pi, or seek to make a social or political statement that the Consortium and WG2 do not intend, as in the case of copyleft. Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? (but it seems some may enjoy it too much.) I am totally mystified by this remark. Perhaps power and responsibility is a burden not a joy. And maybe factors of 2 don't really matter and it doesn't matter whether we use pi or newpi, or consider ASCII as 7-bit or 8-bit. Bob from offline- Oh well, I suppose you convinced me. I just pity all those guys who learned the decimals of Pi - but then again, they will get twice the fun now... LOL
Re: The benefit of a symbol for 2 pi
At 10:06 AM 1/18/2002 -0700, Robert Palais wrote: Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? I think anyone is free to have other competing standards, and there have been other strong ones during the lifecycle of Unicode (ISO 10646 for instance). No one doubts that there are other characters that would be useful to encode. But the original concept of unicode as a 2 byte encoding leaves 64K code points. Unicode as a group quickly found out that was not enough to make everyone happy. As it is, the standard is rife with kluges in the encoding scheme. The limitation of characters to those that are in current use is related in large part to the code point limitations and partially to the desire to prioritize work. It takes the same amount of work to add a character or group of characters regardless of whether or not those characters will be used. there are plenty of characters which exist in the literature that are not ended in Unicode, and in fact are specifically excluded: those of written but dead languages. Newly proposed characters at least have a process: get them in use and addition to Unicode will be easy. In your case, one way to go about that may be to build a (probably pretty straightforward) script that searches out instances of 2pi in tex and word files, etc., and replaces them with newpi references. Create a font which has this character (maybe where the pi is now, or as a user defined char?). Make it easy for folks to get and use these tools. Soon there either will or will not be a substantial body of literature using newpi instead of pi, and a large discussion of why and how its adoption in math texts should happen. Once that is in place, I do not think you will be disappointed by the Unicode group. Right now newpi seems like a meme that is likely to die to the Unicode folks. Show otherwise, and life will be easy, as it was for the euro proponents. Best, Barry Caplan www.i18n.com -- coming soon, sign up for features and launch announcements
Re: The benefit of a symbol for 2 pi
At 10:06 -0700 2002-01-18, Robert Palais wrote: Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? Unicode is for the exchange of data. If there is only one user of the di-pi, then there is no need to exchange the data. I mean, I'd be impressed if there were 50 documents that used the di-pi. So far we've heard of three. Is it unreasonable that we expect to know whether a character is actually useful before we encode it? -- Michael Everson *** Everson Typography *** http://www.evertype.com
Re: The benefit of a symbol for 2 pi
On Fri, 18 Jan 2002 [EMAIL PROTECTED] wrote: I think the Unicode Consortium and WG2 do understand this, and that is why they are so reluctant to encode symbols that do not have established usage, as in the case of 2 pi, or seek to make a social or political statement that the Consortium and WG2 do not intend, as in the case of copyleft. This started to annoy me. If the symbols in Unicode make a political statement by being there, then Unicode supports Christianity (U+2626 and others), anti-Christianity (U+FB29), Islam (U+262a), Hippies (U+262e), Communism (U+262d), and Dharma (U+2638). But somehow the symbol of a minor American social movement is unacceptable because it makes a social statement. If that were true (the actual reason it's not encoded is because it's not used), then I would be highly offended. -- David Starner - [EMAIL PROTECTED], dvdeug/jabber.com (Jabber) Pointless website: http://dvdeug.dhis.org When the aliens come, when the deathrays hum, when the bombers bomb, we'll still be freakin' friends. - Freakin' Friends
Re: The benefit of a symbol for 2 pi
Hello Robert and others, I think the Unicode Consortium and WG2 do understand this, and that is why they are so reluctant to encode symbols that do not have established usage, as in the case of 2 pi, or seek to make a social or political statement that the Consortium and WG2 do not intend, as in the case of copyleft. RP Which seems to make Unicode a defender of the status quo. I don't see how that is a bad thing in this case. Setting a standard for encoding characters is mainly about encoding those characters that are used widely and commonly in communication, not about encoding more or less new characters in order to propagate their use, as far as I can see. RP Inaction is as political as action. We are holders of the standards RP for the technology for encoding symbols, and we won't admit new symbols RP until they are widely used... not necessarily the intent, but possibly RP the impact - that evolution of symbolic communication will be hampered? No. As long as there is a private use area, people will have lots of room to use most of the characters they need if they're a little less commonly used. Evolution of symbolic communication will be hampered in exactly the same way as ASCII hampered it, except that ASCII had no room to include extra characters where needed. Philippmailto:[EMAIL PROTECTED] ___ Chaos reigns within / Reflect, repent, and reboot / Order shall return
RE: The benefit of a symbol for 2 pi
Robert Palais wrote: Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? Definitely hampered, if not entirely blocked. But I tend to think that this is rather a general consequence of having a well defined repertoire of characters, rather than a definite policy of Unicode. With traditional means such as pen and paper, we were free to invent and immediately use any kind of new or altered graphical symbols. When typography started, this freedom was definitely reduced, because all new symbols required ahead planning and control over the lead type producers. With computers, each symbol has to be recognized in advance and identified with a numeric code before it can be used. And each time a new symbol is added to the code, all computers worldwide must be aware of it. So, now, the freedom of inventing new signs is at its historical minimum. And, yes: how the list of existing characters is managed, and who does it, and following which criteria, has now become a new little problem of democracy! By some points of view, however, Unicode has been designed to be a little bit more democratic than many other computer character sets that existed before. It contains a couple of relatively subversive features that, in theory, grant a minimum of freedom: 1) Combining characters (such as accents or diacritic modifiers) which allow modifying existing characters in a limited but significant number of ways. (But there also are pre-composite combination such as à, so most platforms did not bother implement them). 2) A large Private Use Areas (PUA) which contains characters whose interpretation is not defined a priori, and that can be used for encoding symbols not otherwise present in the standard. (But there is the problem of how to privately agree with other users on the meaning of these slots, and you must be in control of fonts and rendering engine in order to display your characters). 3) A newly added operator (ZWL) which allows joining two characters into a single unit. (But I don't know of any implementation of this, and it is not supposed to generate new visual symbols, however). 4) A set of operators called Ideographic Description Character (IDC) for specifying the shape of Chinese ideographs which are not part of the standard. (But Unicode merely permits rendering such expressions as if they were actual Chinese ideographs: there is no obligation to do so and, consequently, no implementations exist, as far as I know). These are all small things, compared to the freedom allowed by paper and pen, but you must consider that the computer technology we have been used so far doesn't even grant these. _ Marco
Re: The benefit of a symbol for 2 pi
At 01:45 PM 1/18/2002 -0500, you wrote: The limitation of characters to those that are in current use is related in large part to the code point limitations What limitations? We have over a million codepoints to play with. There is plenty of room. I've always been under the impression that one of the original goals of the Unicode effort was to do away with he sort of multi-width encodings we are all too familiar with (EUC, JIS, SJIS, etc.). this was to be accomplished by using a fixed width encoding. In my mind, everything other than that in order to increase space (but not necessarily to save bandwidth) is a kluge, and a compromise, because it means code still has to be aware of the details of the the encoding scheme. I do not dispute that with the kluges/compromises, there is plenty of room. There are plenty of characters which exist in the literature that are not ended in Unicode, and in fact are specifically excluded: those of written but dead languages. They are not only not excluded, they are included: Runic and Deseret are just the beginning. There are many pending proposals for things like hieroglyphs and cuneiform. Now that there are kluges that allow for extra room. But wasn't it not always the case historically speaking that these languages were, shall we say, less than welcome?
Re: The benefit of a symbol for 2 pi
At 10:06 AM 1/18/02 -0700, Robert Palais wrote: Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? What is missing from this position is a recognition of the *irreversability* of character encoding. Symbols that do not have established use (no matter how worthwhile they are) have a frighteningly high risk of never becoming accepted - meaning that a code position has been used up and cannot ever be used for something that people actually use (whether now or later). Furthermore, there is a small cost of 'carrying a character on the books', as each character added will incrementally grow the size of support files that Unicode implementations will need. Carrying such costs for rarely used characters, is a tradeoff people find acceptable. Carrying the cost (for ever) for 'oops we don't need this one after all' mistakes, is acceptable to no-one. Untested innovations have a better than 0 chance of being in the latter category. Mathematics is a field where ad-hoc notation is rampant (esp. in new sub-disciplines) and experimentation abounds. Unicode usually waits until there is evidence that a notation has settled before adding the new symbols. While this won't eliminate the chance that some symbols become obsolete over time, it does ensure that there always is a body of historical texts using that symbol - so a character would at a minimum have historical significance and be used by historians of science re- producing older papers. An untested innovation does not have even that saving grace. None of these arguments invalidate the *mathematical* reasoning behind the desire to adopt a better notation. Physicists have long done that by defining hbar to be h over 2pi, reducing three symbols and a fraction into one. Once the new '2pi' has been used in enough mathematical monographs it will become a prima facie candidate for review for new encoding, like all new mathematical notation - but not before then. A./
Re: The benefit of a symbol for 2 pi
At 11:02 -0800 2002-01-18, Barry Caplan wrote: There are plenty of characters which exist in the literature that are not ended in Unicode, and in fact are specifically excluded: those of written but dead languages. They are not only not excluded, they are included: Runic and Deseret are just the beginning. There are many pending proposals for things like hieroglyphs and cuneiform. Now that there are kluges that allow for extra room. But wasn't it not always the case historically speaking that these languages were, shall we say, less than welcome? What do you mean, less than welcome? By whom? It's always been intended to be the Universal Character Set. -- Michael Everson *** Everson Typography *** http://www.evertype.com
RE: The benefit of a symbol for 2 pi
Just an aside on terminolgy: At 08:02 PM 1/18/02 +0100, Marco Cimarosti wrote: 3) A newly added operator (ZWL) which allows joining two characters into a it's CGJ for Combinign Grapheme Joiner 4) A set of operators called Ideographic Description Character (IDC) for They are for Ideographic Description Sequences, for which IDS is the abbreviation. A./ PS: I liked the arguments about the effect of technology on the evolution of writing systems.
Re: The benefit of a symbol for 2 pi
On Fri, Jan 18, 2002 at 11:35:44AM -0800, Asmus Freytag wrote: Furthermore, there is a small cost of 'carrying a character on the books', as each character added will incrementally grow the size of support files that Unicode implementations will need. They will also end up in fonts that attempt full coverage - and not nessecarily full Unicode coverage, either. A new mathematical character will end up in MES-3 (IIRC) and indirectly on the requirements list of some buyers. Any one trying to make a full mathematical font will probably pull in all the characters from the matematical blocks; after all, how many people can look at a character and say whether it's common, but outside their knowledge, rare, or not used? It will probably end up mathematical requirement lists for fonts and programs - it's so much easier to say all the mathematical characters rather then to try and pick the ones your department may need from the one's they won't. -- David Starner - [EMAIL PROTECTED], dvdeug/jabber.com (Jabber) Pointless website: http://dvdeug.dhis.org When the aliens come, when the deathrays hum, when the bombers bomb, we'll still be freakin' friends. - Freakin' Friends
Re: The benefit of a symbol for 2 pi
R. Palais wrote... Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? Hmmm. I almost want to say gimme a break! This isn't a matter of political stances or hampering or censorship, it is a matter of division of labor and project goals. It still appears that some people aren't understanding who has what jobs and what the goals are. It is a mathematician's job to do math, and that can involve inventing whatever new symbols may be needed along the way. Fine. It is our job as a standarizing organization to standardize what is IN USE so that (as a goal) people can standard-ly communicate those symbols internationally without ambiguity. It is _NOT_ our job, and never will be our job, to invent new symbols or rally around new symbols that we think are cool or useful in any particular branch of study and then promote their use. This is the same situation as having one person in town be the mural painter and another be the news photographer. Is every news photographer required to paint murals, too, or be otherwise accused of hampering artistic evolution? It is not that we defend the status quo or stand by some principled inaction with regard to symbol invention, or have some grand political stance against the invention of new symbols. We add symbols to the standard all the time! That's our job: we collectively decide what symbols are used widely enough to be worth encoding, and then add them to the standard. What would be the point for us to add a faddish or other nouveau symbol that tops the popularity charts this week, but which goes out of fashion next week and for the next hundred years is never used and just becomes another blob in the code charts and data tables for people to worry about? Rick
Re: The benefit of a symbol for 2 pi
Which seems to make Unicode a defender of the status quo. Inaction is as political as action. We are holders of the standards for the technology for encoding symbols, and we won't admit new symbols until they are widely used... not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? Ooh, throwing red meat to the lions! When speaking of status quo ante, it is important to keep in mind the perspective you have on the matter. The status quo for most Unicode developers was the existence of a large, and proliferating collection of overlapping, incomplete, and only partially interoperable character encodings (numbering in the multiple hundreds) that made internationalization engineering a mess and which resulted in countless opportunities for data corruption when attempting to operate in a global information context. Furthermore, many useful characters, including some national scripts and many minority and historic scripts, were completely unrepresentable in any significant character encoding standard, and required local hacks based on fonts, typically non-communicable in email, on the web, or in common document formats. In that context, the Unicode manifesto was a revolutionary one, in that it basically advocated junking the established approach, and deliberately flew in the face of the established, standard framework for extending character sets -- ISO 2022. And the developers of Unicode deliberately created a development organization -- a cabal, if you will -- outside the ISO framework, to pursue the vision. As for many successful revolutions, the original ideals have been compromised and battered a bit in the resulting struggle, and the new ideas have begun to take on the patina of establishment as they succeed. The revolutionaries themselves have become pragmatists and compromisers -- at least the ones still involved -- since they value success of the overall revolution over ideological purity at the end of the day. On the other hand, it is also true that the Unicoders are typically rather conservative when it comes to the actual encoding of writing systems that they do. As Michael Everson pointed out, this is partly a natural result of a shared belief that Unicode should encode characters that are in use, and thereby known to be useful. It has been reinforced by over a decade's worth of experience in encountering collections of stuff that might, by some stretch of someone's imagination, be characters, but without much evidence of real use for any significant textual interchange. The conservatism is also a result of the need to maintain credibility in what is presented for encoding, since part of the compromise over the years has now resulted in the Unicode Consortium working hand in glove with ISO to promote and extend the joint standards, rather than butting heads with ISO in competition to create rival standards. From this point of view, it is easy to see how the Unicode Consortium could end up being seen as an obstructionist organization dedicated to the status quo. If your passion is as a script reformer -- or even just to overturn something in a little way by introducing a new symbol to improve something, then you need all the traction you can muster, since writing systems, orthographies, symbol conventions, and the like are well-entrenched cultural systems with lots of inertia, and are very difficult to change significantly. And since the Unicode Consortium is busy promoting a successful worldwide character encoding, it seems a natural to come knocking on the door with your new script, new orthography, or new basketful of symbols, since if they get into the successful, universal character encoding, you increase your chances of succeeding in the writing system reform. Yet the big, bad, Character Academy and its panjums close the doors and say, No writing system reformers need apply! So they become part of the problem -- part of the inertia which is standing in the way of the obvious, logical improvement that the reformer has in hand. What it comes down to, basically, is that the Unicode Consortium does not view writing system reform, spelling reform, writing convention reform, choice of alphabets, or the introduction of new systems or new symbols as part of its charter. Those are battles for other groups to deal with, in whatever the appropriate forums may be. Instead, the Unicode Consortium views character encoding reform to be its charter. But it is understandable how it might not be self-evident to those not deeply involved in the work of the encoding, where the boundaries of character encoding reform might be, nor why the UTC eagerly latches on to some proposals as being in scope and turns down others as out of scope. not necessarily the intent, but possibly the impact - that evolution of symbolic communication will be hampered? One last point. While it may be true that standardization of a character in Unicode makes it
Re: The benefit of a symbol for 2 pi
This is the same situation as having one person in town be the mural painter and another be the news photographer. Is every news photographer required to paint murals, too, or be otherwise accused of hampering artistic evolution? That seems to be the wrong analogy. The question is whether the news photographer photographs the mural. Certainly looking at the US for profit news media, vs. say, the BBC, it is obvious that it matters. I didn't want unicode people to do math, but it might even be apparent to those who encode symbols that the overwhelming usage of the single symbol pi is in the conceptually natural combination 2 pi (are there any other examples) and this would better be done in half as many bits ;-) The two points below raise the question to me, is popularity/use the criterion or not. From one hand, I am hearing that it is THE criterion, and from another it is not. I've always felt the majority is not always right, nor is history. I'd even support the inclusion of a copyleft symbol ahead of \newpi! Bob That's our job: we collectively decide what symbols are used widely enough to be worth encoding, and then add them to the standard. What would be the point for us to add a faddish or other nouveau symbol that tops the popularity charts this week, but which goes out of fashion next week and for the next hundred years is never used and just becomes another blob in the code charts and data tables for people to worry about? Rick
RE: The benefit of a symbol for 2 pi
Oh my! I have to agree, the discussion on the impact of symbol uniformization IS extremely enlightening to me, although I'm somewhat apologetic again from distracting everyone from more serious and practical issues. Thank you all for your thoughtful responses, both on and off-group! On Fri, 18 Jan 2002, Asmus Freytag wrote: 3) A newly added operator (ZWL) which allows joining two characters into a it's CGJ for Combinign Grapheme Joiner 4) A set of operators called Ideographic Description Character (IDC) for They are for Ideographic Description Sequences, for which IDS is the abbreviation. A./ PS: I liked the arguments about the effect of technology on the evolution of writing systems.
Re: The benefit of a symbol for 2 pi
David Starner wrote: If the symbols in Unicode make a political statement by being there, then Unicode supports Christianity (U+2626 and others), anti-Christianity (U+FB29), Islam (U+262a), Hippies (U+262e), Communism (U+262d), and Dharma (U+2638). Ahem... Not to mention Turtles. ;-) Rick
Re: The benefit of a symbol for 2 pi
At 11:36 AM 1/18/02 -0800, Rick McGowan wrote: It is our job as a standarizing organization to standardize what is IN USE so that (as a goal) people can standard-ly communicate those symbols internationally without ambiguity. It is _NOT_ our job, and never will be our job, to invent new symbols or rally around new symbols that we think are cool or useful in any particular branch of study and then promote their use. In fact: The only time where we have added a recently invented symbol that we knew *not* yet to be in any actual use, was the euro symbol. This was not a revolutionary act ;-) on our part, but reflected the creditable representation by the European Commission that its use would be required in the very near future. If the American Mathematical Society (arguably the currently most influential publisher of mathematical papers world wide) were to institute a policy that from a given date, all manuscripts were required to use the symbol for 2 pi, instead of 2*pi -- in that hypothetical case, such a symbol could potentially be encoded before it's in actual use, especially if that move had resonated well in the math community and other publisher were likely to follow it. What distinguishes the real and hypothetical case set forth here, from the proposal at hand is a creditable commitment on part of a large and identifiable user community to begin use of a symbol, as soon as it is available. Even so, the situation would feel to the character encoding community as a very exceptional situation, fraught with residual risk of early obsolescence of the character. Why don't we postpone the rest of this discussion until the day it comes back with the kind of endorsements suggested in the case studies. A./
Re: The benefit of a symbol for 2 pi
Robert Palais wrote, I'd even support the inclusion of a copyleft symbol ahead of \newpi! Has there been any consideration of practical alternatives, such as selecting a lookalike or similar character from the plethora of those already encoded and promoting its use to represent the newpi character? Some possibilities which come to mind are: The Greek letter(s) SAMPI, which is a PI turned sideways, comes in two flavours, capital and small. U+03E0 and U+03E1, or in UTF-8, Ϡ and ϡ. The Cyrillic letter SHA, capital and small at U+0428 (Ш) and U+0448 (ш). (Well, it probably looks too much like Roman Numeral Three at U+2162 (Ⅲ).) But, another Cyrillic letter looks like an upside-down PI with a tail, U+040F (Џ) which is Cyrillic DZHE. Remote possibilities might include Reversed pilcrow (⁋) U+204B, Peso sign at U+20B1 (₱), Double-struck capital PI at U+203F (ℿ), Element of Opening Downwards at U+2AD9 (⫙), Yi Syllable CUOP at U+A2BC (ꊼ). Or, since the newpi glyph could be considered as a ligature of PI and PI, perhaps the character should be formed by U+03C0 plus U+200D plus U+03C0? Best regards, James Kass.
Re: The benefit of a symbol for 2 pi
This discussion has sparked a few lively contributions and brought up some important points, so even though it may have been beaten to death and Robert has announced his intent to move it to another forum, I still have some comments that may be pertinent in the AMS discussion. I was a little disappointed that others were drawn into the debate over the relative merits of the constants 3.14 versus 6.28, since this issue is completely irrelevant to the question of encoding a new 2 pi symbol in Unicode. For most of us, at least, the objection to encoding this symbol in Unicode has nothing at all to do with its theoretical usefulness, but its lack of currency at the present time. Whether the symbol would be useful or represents an important mathematical constant is not the point. It must be commonly used, or at least recognized, within the field. It is not a question of whether typographers would personally see the benefit of such a symbol (BTW, not all of us are typographers; this list also includes software developers, linguists, and standardization types). The symbol must already be in use, as determined by a sufficient body of work. Mathematicians are researchers; they know it is not sufficient to cite a single article, especially one written by oneself or one's associates, as a body of work to demonstrate the use or non-use of something. The 2 pi symbol is an experiment, and it is important to remember that not all experiments are successful! Some proposed characters, words, ideas, TV shows, etc. do not achieve a sufficient level of popularity and are discarded. As Rick McGowan indicated, it is not a goal of Unicode to encode characters that someone, even a lot of people, believe *might* (or should) achieve widespread use; they must already be in use (with one notable exception; see below). Think of a dictionary. New words are invented all the time, sometimes intentionally by companies or advertisers, yet nobody would think of going to Merriam-Webster and asking them to include their newly invented word in the next edition of the dictionary so that it will be recognized and will gain greater use. Rather, the word has to gain a certain degree of acceptance *before* it is enshrined in the dictionary. The same is true for encoding characters in Unicode. If Dr. Beebe suggested trying to get the 2 pi character into Unicode to stimulate its adoption, then he does not understand the principles and policies of Unicode. I wonder if there is a perception, because of the extensive work done by the Unicode Consortium and ISO/IEC JTC1/SC2/WG2 in encoding over 95,000 characters, that any newly invented character or symbol can be encoded just for the asking. The fact is that there are over 95,000 characters in Unicode, not because the relevant committees are fast and loose in encoding newly invented characters, but because there really are that many well-attested characters in the world. (Well, OK, minus some of the compatibility characters.) David Starner mentioned the proposed copyleft sign. This was a reversed copyright sign (roughly representable by U+0254 plus U+20DD) which enjoys some use by the Free Software Foundation and the GNU project to signify a legal agreement that is similar to, but different from, a traditional copyright. The symbol is apparently recognized by many adherents to the free software movement, probably more people than would recognize the 2 pi symbol. But it turned out to be used primarily as a logo to promote the movement, rather than as a plain-text character to indicate the legal status of a work, as U+00A9 COPYRIGHT SIGN would be. In fact, it would almost certainly not be recognized at all by non-FSF, non-GNU people except as a whimsical play on the copyright sign (the suggested name demonstrated the anti-copyright religion of the proponents). The classic exception to the principle that a symbol must be in current use before it can be encoded is U+20AC EURO SIGN. This character was encoded in Unicode 2.1 in 1998, long before most people -- including those who are now converting their money to euros -- had ever seen it. But there was a difference: the Euro sign was invented by, and had the full support of, the European Monetary Union, and was *guaranteed* to become a commonly used symbol, something that cannot normally be said of most newly invented symbols. Even though the symbol had never been used before, there was no question that it would catch on. A good measure of whether the 2 pi symbol has become sufficiently well recognized to be added to Unicode is whether it can be used in works like the JOMA article without having to explain or justify its usage beyond that which would be needed for any other symbol. I hope that this discussion has shed some light on an important principle of Unicode for Robert (and perhaps for others), so that the AMS discussion can proceed in a productive manner. The
Re: The benefit of a symbol for 2 pi
On Thu, 17 Jan 2002 [EMAIL PROTECTED] wrote: I'm not sure I see anything new here. However, as I suggested, Dr. Beebe's intention was to bring the character to the discussion within the mathematical community where its potential for usefulness MIGHT be sufficient to encourage its appearance and use enough to then merit inclusion in the AMS' unicode recommendations. I apologize again if my misunderstanding that I was advised to bring it up directly here offended you, and gave a false impression of Dr. Beebe's I'm sure adequate understanding of the nature of the purposes of unicode. I will be unsubscribing, so please address future correspondence to me directly. Best regards, Bob important points, so even though it may have been beaten to death and Robert has announced his intent to move it to another forum, I still have some comments that may be pertinent in the AMS discussion. If Dr. Beebe suggested trying to get the 2 pi character into Unicode to stimulate its adoption, then he does not understand the principles and policies of Unicode. I wonder if there is a perception, because of the extensive work done by the Unicode Consortium and ISO/IEC JTC1/SC2/WG2 in encoding over 95,000 characters, that any newly invented character or symbol can be encoded just for the asking. The fact is that there are over 95,000 characters in Unicode, not because the relevant committees are fast and loose in encoding newly invented characters, but because there really are that many well-attested characters in the world. (Well, OK, minus some of the compatibility characters.) I hope that this discussion has shed some light on an important principle of Unicode for Robert (and perhaps for others), so that the AMS discussion can proceed in a productive manner. The bottom line, however, will certainly be that Robert's 2 pi symbol is no Euro sign, with a guarantee of future utility; it will have to demonstrate that utility before being encoded. -Doug Ewell Fullerton, California
RE: The benefit of a symbol for 2 pi
Robert Palais wrote: Thanks, good suggestion! Don Tucker pointed out the stability of a three-legged stool. It has to be one-syllable, though tri does have a certain 3-ness to it. Right on! It sure does, even more, tri is how number 3 is pronounced in many Slavic languages. You would sure produce a lot of jokes, let alone confusion. Like III/2 r^2 when spoken would be heard like 3/2 r^2... And it's not even a good approximation since tri is close to 6, not to 3... I suppose newpi is not bad at all. Eventually, as it becomes widely used, the people will drop the new part themselves (well, let's hope they won't drop the pi:). I'd be curious if you disagree with the thesis that a symbol for 6.28 has scientific/mathematical merit (in comparison 3.14...), and if so why? 3.14... is to a circle what 4 is to a square. It is the relationship between the diameter and the circumference. The fact that the number 2 appears in many formulas does not make it bad. I even welcome it, because 2 pi is something that stands out and immediately suggests circles and angles. You can call it inertia, but you have to agree that 2x is more special than Y. Well, it is to me anyway. Anyway, good luck with the newpi efforts, and may the best pi win! ;) Lars
Re: The benefit of a symbol for 2 pi
At 14:08 -0600 2002-01-16, David Starner wrote: On Wed, Jan 16, 2002 at 11:33:48AM -0700, Robert Palais wrote: is at the same time somewhat a Catch-22. Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. It's too late for Unicode 3.2. In any case, there's a lot of people who would like to add a character or script to Unicode. (I'd personally like a LATIN CAPITAL LETTER L WITH BELT, myself, What for? and some Free Software people were pushing for a copyleft sign. As I recall they failed to meet some criteria. And the pun is STILL bad and untranslatable. The opposite of copyright would be copywrong. :-) -- Michael Everson *** Everson Typography *** http://www.evertype.com
Re: The benefit of a symbol for 2 pi
At 13:12 -0700 2002-01-16, Robert Palais wrote: It was also accepted in use in the Mathematical Association of America's refereed Journal of Online Mathematics www.joma.org/more/palaismore.html where the one revolution periodicity and 1/4 phase shifts are represented and the graphs are labelled more simply with this symbol. In more than one article? It is referenced in the Springer - Mathematical Intelligencer article, and in the Journal of Online Math article. I haven't seen the Lithuanian reprinting yet! No, I mean has more than one author put it in print in more than one publication, and if so, how many and how many? -- Michael Everson *** Everson Typography *** http://www.evertype.com
[OT] Geometric trivia (was RE: The benefit of a symbol for 2 pi)
Lars Kristan wrote: 3.14... is to a circle what 4 is to a square. More generally, 3.1415... is to a circle what all numbers in from 2.8284... to 4 are to a square. _ Marco
RE: The benefit of a symbol for 2 pi
Lars Kristan wrote: 3.14... is to a circle what 4 is to a square. It is the relationship between the diameter and the circumference. No it is NOT, mathematically. The square whose Perimeter is 4 has diameter \sqrt 2. What is the side of a circle? It shows that the problem is so ingrained that it is almost invisible and that many people cannot imagine that \pi is not perfect. (Note however that the inscribed hexagon, six equilateral triangles of side 1, gives an immediate estimate that \newpi is greater than, and close to 6. (Thanks to Prof. Cherkaev) If the discussion must persist, I will wait to respond to such attempts to argue the mathematical point (which don't belong here. Observing your discussions, I do wonder if the participants recognize the responsibility of their influence upon ideas, through symbols (but it seems some may enjoy it too much.) Speaking of adding words to the dictionary, it did bring to mind the word eumemics which is to memes as eugenics is to genes. Anyway, the point being while a symbol such as f may not have a specific concept associated with it, \pi and \newpi do, important enough that broadcast of \pi to the heavens was supposed to prove our intelligence. They'll get a laugh. Yes, Pi IS the ratio of circumference to diameter, but that was the last time anyone ever saw or used diameter, \newpi is the circumference of the unit (radius) circle, which is used exclusively in mathematics. Hence all the MEANINGLESS 2s. My point was not that formulas involving 2 \pi are incorrect, but that they, and formulas derived by then separating the 2 and the \pi are not economical of meaning. To me it is like writing 2+2 instead of 4 everywhere, or changing the value of Euler's other number e. Lots of meaningless factors would follow. The fact that the number 2 appears in many formulas does not make it bad. I even welcome it, because 2 pi is something that stands out and immediately suggests circles and angles. You can call it inertia, but you have to agree that 2x is more special than Y. Well, it is to me anyway. Anyway, good luck with the newpi efforts, and may the best pi win! ;) Lars
RE: The benefit of a symbol for 2 pi
From: Robert Palais [EMAIL PROTECTED] To: Lars Kristan [EMAIL PROTECTED] CC: [EMAIL PROTECTED] Subject: RE: The benefit of a symbol for 2 pi Date: Thu, 17 Jan 2002 10:11:37 -0700 (MST) Lars Kristan wrote: 3.14... is to a circle what 4 is to a square. It is the relationship between the diameter and the circumference. No it is NOT, mathematically. The square whose Perimeter is 4 has diameter \sqrt 2. What is the "side" of a circle? It shows that the problem is so ingrained that it is almost invisible and that many people cannot imagine that \pi is not perfect. (Note however that the inscribed hexagon, six equilateral triangles of side 1, gives an immediate estimate that \newpi is greater than, and close to 6. (Thanks to Prof. Cherkaev) If the discussion must persist, I will wait to respond to such attempts to argue the mathematical point (which don't belong here. Observing your discussions, I do wonder if the participants recognize the responsibility of their influence upon ideas, through symbols (but it seems some may enjoy it too much.) Speaking of adding words to the dictionary, it did bring to mind the word "eumemics" which is to "memes" as eugenics is to genes. Anyway, the point being while a symbol such as "f" may not have a specific concept associated with it, \pi and \newpi do, important enough that broadcast of \pi to the heavens was supposed to prove our intelligence. They'll get a laugh. Yes, Pi IS the ratio of circumference to diameter, but that was the last time anyone ever saw or used diameter, \newpi is the circumference of the unit (radius) circle, which is used exclusively in mathematics. Hence all the MEANINGLESS 2s. My point was not that formulas involving 2 \pi are incorrect, but that they, and formulas derived by then separating the 2 and the \pi are not economical of meaning. To me it is like writing 2+2 instead of 4 everywhere, or changing the value of "Euler's other number" e. Lots of meaningless factors would follow. As for all this about radian measure: 1. Design a machine to indicate the number of revolutions through which a wheel has turned. Easy. 2. Design a machine to indicate the number of RADIANS through which a wheel has turned. Can it be done?? (Using a 355:113 gear ratio is cheating.) _ $B%a!<%k%5!<%S%9$O!"@$3&(B No.1 $B$N(B MSN Hotmail $B$G!*(Bhttp://www.hotmail.com/JA/
Re: The benefit of a symbol for 2 pi
On Wed, Jan 16, 2002 at 10:13:31AM -0700, Robert Palais wrote: The pi problem turns something which should be natural into memorization for many students, and Unicode could allow an alternative to eventually correct it. Unicode is generally not the place for evangalism. [T]he Unicode Standard does not encode idiosyncratic, personal novel, [or] rarely exchanged ... characters, and I'm afraid as of yet, your double pi symbol is all of those. Get it in use, and then the Unicode standard will encode it. I can not speak for Unicode, and there's some small chance that they might disagree with me. In that case, you should look up the procedures on making a formal proposal. -- David Starner - [EMAIL PROTECTED], dvdeug/jabber.com (Jabber) Pointless website: http://dvdeug.dhis.org When the aliens come, when the deathrays hum, when the bombers bomb, we'll still be freakin' friends. - Freakin' Friends
Re: The benefit of a symbol for 2 pi
On Wed, 16 Jan 2002, Michael Everson wrote: I think it's cute. But I guess I'd call it tri. -- Michael Everson *** Everson Typography *** http://www.evertype.com Thanks, good suggestion! Don Tucker pointed out the stability of a three-legged stool. It has to be one-syllable, though tri does have a certain 3-ness to it. David Starner's constructive suggestion: Get it in use, and then the Unicode standard will encode it. is at the same time somewhat a Catch-22. Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. I'd be curious if you disagree with the thesis that a symbol for 6.28 has scientific/mathematical merit (in comparison 3.14...), and if so why? I was hoping someone would contend this point when it was published, since I am interested to learn any conceptual advantages of 3.14... other than historical inertia, but no one did. Historical inertia prevents elimination of the error, but I'm just suggesting an alternate might be nice. The Lituanian Math Journal asked to translate and reprint it, although that probably doesn't qualify as in use. It was also accepted in use in the Mathematical Association of America's refereed Journal of Online Mathematics www.joma.org/more/palaismore.html where the one revolution periodicity and 1/4 phase shifts are represented and the graphs are labelled more simply with this symbol. The response to the article chosen for publication also notes the evangelical (somewhat tongue-in-cheek) tone: I agree with Bob Palais' \pi -ous article but it might be 2 \pi- ous :-)
Re: The benefit of a symbol for 2 pi
I think it's cute. But I guess I'd call it tri. -- Michael Everson *** Everson Typography *** http://www.evertype.com
Re: The benefit of a symbol for 2 pi
Robert Palais wrote: Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. Speaking not officially, but as someone who has been lurking around here awhile, the Unicode Technical Committee does not generally float trial balloons. In other words, UTC doesn't look around for graphical symbols which, on a theoretical basis might be nice or even useful to someone, and then encode them in the hope that they will become widely used. UTC looks around for symbols that are in wide enough use to warrant being encoded. If this symbol starts showing up widely instead of 2 pi in mainstream high school math text books, then UTC will know it's time to encode it. Until then, it's a curiosity. Rick
Re: The benefit of a symbol for 2 pi
At 11:33 -0700 2002-01-16, Robert Palais wrote: It was also accepted in use in the Mathematical Association of America's refereed Journal of Online Mathematics www.joma.org/more/palaismore.html where the one revolution periodicity and 1/4 phase shifts are represented and the graphs are labelled more simply with this symbol. In more than one article? -- Michael Everson *** Everson Typography *** http://www.evertype.com
Re: The benefit of a symbol for 2 pi
On Wed, Jan 16, 2002 at 11:16:51AM -0800, Rick McGowan wrote: If this symbol starts showing up widely instead of 2 pi in mainstream high school math text books, then UTC will know it's time to encode it. Until then, it's a curiosity. That's a little excessive, isn't it? I would think that maybe 100 publications by a dozen authors, and evidence of continuing use might be enough to start serious discussion of encoding it. I mean, I'm within 12 hours of B.S. in Mathematics, and I haven't seen half the symbols in the Mathematical Operators section outside the standard, much less in a high school textbook. -- David Starner - [EMAIL PROTECTED], dvdeug/jabber.com (Jabber) Pointless website: http://dvdeug.dhis.org When the aliens come, when the deathrays hum, when the bombers bomb, we'll still be freakin' friends. - Freakin' Friends
Re: The benefit of a symbol for 2 pi
Thanks Rick,
That's why I brought it up here, to get unofficial feedback!
As a matter of credit- the suggested \newpi symbol was not mine but
due to Richard Palais (mathematical adviser of Leslie Lamport (LaTeX)
and Mike Spivak (AMSTeX/Joy of TeX) at Brandeis). In \TeX :
\def \newpi{{\pi\mskip -7.8 mu \pi}}
suffices. My only suggestion was that Unicode offer its users a
single symbol for one of the fundamental constants of math and
natural science, the circumference of the unit circle, 6.28...
Most people think \pi seem to think \pi was an ancient Greek invention.
The historical accident of 3.14... is described in the article, and dates
to the 1700's - the Euler chose to simplify Periphery/Diameter, in their
Greek spellings, \pi \over \delta rather than the competing
Periphery/Radius, or \pi \over \rho
Bob
On Wed, 16 Jan
2002, Rick McGowan wrote:
Robert Palais wrote:
Nelson Beebe recommended it since he figured unicode 3.2 would be
the make or break for getting it in use.
Speaking not officially, but as someone who has been lurking around here
awhile, the Unicode Technical Committee does not generally float trial
balloons. In other words, UTC doesn't look around for graphical symbols
which, on a theoretical basis might be nice or even useful to someone,
and then encode them in the hope that they will become widely used. UTC
looks around for symbols that are in wide enough use to warrant being
encoded.
If this symbol starts showing up widely instead of 2 pi in mainstream
high school math text books, then UTC will know it's time to encode it.
Until then, it's a curiosity.
Rick
Re: The benefit of a symbol for 2 pi
On Wed, Jan 16, 2002 at 11:33:48AM -0700, Robert Palais wrote: is at the same time somewhat a Catch-22. Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. It's too late for Unicode 3.2. In any case, there's a lot of people who would like to add a character or script to Unicode. (I'd personally like a LATIN CAPITAL LETTER L WITH BELT, myself, and some Free Software people were pushing for a copyleft sign.) Proof of use is one way that Unicode keeps the requests down to a dull roar. I'd be curious if you disagree with the thesis that a symbol for 6.28 has scientific/mathematical merit (in comparison 3.14...), and if so why? In an abstract sense, I can't disagree with your arguments, any more than I can disagree with the fact that English should use an alphabet/orthography that consistently distinguishes between vowel sounds. But while introducing the tri is simpler than revising English's orthography, it still comes off as one of those reform schemes that are more trouble than they're worth. Have you considered using a preexisting symbol? The Cyrillic section of Unicode has a bunch of symbols distinct from current math symbols that fit in with the Greek/Latin characters currently used. Say, 0416, or 0418, or 0409, or 044E. It was also accepted in use in the Mathematical Association of America's refereed Journal of Online Mathematics www.joma.org/more/palaismore.html where the one revolution periodicity and 1/4 phase shifts are represented and the graphs are labelled more simply with this symbol. This is more important. If there are a number of uses and a number of users, especially in formal, edited or refereed sources, then Unicode is much more likely to encode. But one source isn't enough - I can come up with a bunch of new characters with one or more sources in a few hours. -- David Starner - [EMAIL PROTECTED], dvdeug/jabber.com (Jabber) Pointless website: http://dvdeug.dhis.org When the aliens come, when the deathrays hum, when the bombers bomb, we'll still be freakin' friends. - Freakin' Friends
Re: The benefit of a symbol for 2 pi
At 11:33 AM 1/16/2002 -0700, Robert Palais wrote: is at the same time somewhat a Catch-22. Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. I'd be curious if you disagree with the thesis that a symbol for 6.28 has scientific/mathematical merit (in comparison 3.14...), and if so why? My guess is that since pi is the ratio of the circumference to the diameter, that the diameter is a more natural conception of the size of a circle than the radius. Of course mathematically, it doesn't matter other than the factor of 2. But other geometrical shapes, particularly polygons, are measured by line segments that extend from one point to another on the same shape, or series of shapes. A radius just sort of ends in the middle, while a diameter or other chord begins and ends on the circle. I can't quote the history, but if I imagine back to the Greek days, I bet the diameter was the primary measure. Other polygonal shapes with which they were familiar had their measures in terms of a line segment crossing the entire shape and touching the boundaries, or coincident with the boundary. Mathematicians pondering the circle for the first time, there probably was no reason to think otherwise. How to proceed from there to figure the area of a circle or the ratio of the diameter to the circumference were probably some of the greatest challenges of the day. They wanted to know the circumference and area, same as they had calculated for other shapes. I would guess that since pi is the ratio of the circumference and diameter, that this problem was solved first. Had it been the other way around, our formulas might look the way Dr. Palais suggests. Now that I think about it, I wonder if the very concept for radius grew out of the solution to the area of the circle: was the original formula A = pi * (d over 2)squared? If so, then maybe a conceptual leap was made to simplify it, thus inventing the radius. Why simplify the d/2 part and not the other way (pi/4)? Probably because pi is just a number, while d/2 turned out to have some connection to the physical world - the distance from the edge of a circle to the center. But this is just idle lunchtime speculation on my part. Note that using the new symbol the circumferance of a circle is simply tri*r, but the Area changes form pi*r(squared) to tri *(1/2) times r squared, so you lose as much as you gain it seems to me. Barry Caplan
Re: The benefit of a symbol for 2 pi
I thought this would best be kept offline, but I disagree with most of these points, where I could see many in your first private email. If you read the article, you will see that there is basically no use of diameter in mathematics or physics, that pi is an invention of the 1700's, not the greeks, and that in fact, regarding the area formula, we have noticed that you gain by the factor of 1/2 natural for all other quadratics - 1/2 m v ^2 . 1/ 2 g t^2, 1/2 k x^2. p^2 / 2 m, etc. I apologize to the unicode people and realize that here is NOT the best place for these aspects of the discussion. Without doubt, 2 \pi is the most widely used form of use of \pi, with no valid purpose except historical convention. Many numerical analysts/scientific computers begin their codes by defining a constant equal to 6.28... to simplify their codes, and I thought typographers might see the value of such an option for simplicity as well. Apparently I was wrong. Rather than use a new character, using the \TeX macro is easy enough for most of those in the mathematical community who use some version of \TeX. On Wed, 16 Jan 2002, Barry Caplan wrote: At 11:33 AM 1/16/2002 -0700, Robert Palais wrote: is at the same time somewhat a Catch-22. Nelson Beebe recommended it since he figured unicode 3.2 would be the make or break for getting it in use. I'd be curious if you disagree with the thesis that a symbol for 6.28 has scientific/mathematical merit (in comparison 3.14...), and if so why? My guess is that since pi is the ratio of the circumference to the diameter, that the diameter is a more natural conception of the size of a circle than the radius. Of course mathematically, it doesn't matter other than the factor of 2. But other geometrical shapes, particularly polygons, are measured by line segments that extend from one point to another on the same shape, or series of shapes. A radius just sort of ends in the middle, while a diameter or other chord begins and ends on the circle. I can't quote the history, but if I imagine back to the Greek days, I bet the diameter was the primary measure. Other polygonal shapes with which they were familiar had their measures in terms of a line segment crossing the entire shape and touching the boundaries, or coincident with the boundary. Mathematicians pondering the circle for the first time, there probably was no reason to think otherwise. How to proceed from there to figure the area of a circle or the ratio of the diameter to the circumference were probably some of the greatest challenges of the day. They wanted to know the circumference and area, same as they had calculated for other shapes. I would guess that since pi is the ratio of the circumference and diameter, that this problem was solved first. Had it been the other way around, our formulas might look the way Dr. Palais suggests. Now that I think about it, I wonder if the very concept for radius grew out of the solution to the area of the circle: was the original formula A = pi * (d over 2)squared? If so, then maybe a conceptual leap was made to simplify it, thus inventing the radius. Why simplify the d/2 part and not the other way (pi/4)? Probably because pi is just a number, while d/2 turned out to have some connection to the physical world - the distance from the edge of a circle to the center. But this is just idle lunchtime speculation on my part. Note that using the new symbol the circumferance of a circle is simply tri*r, but the Area changes form pi*r(squared) to tri *(1/2) times r squared, so you lose as much as you gain it seems to me. Barry Caplan
Re: The benefit of a symbol for 2 pi
To the members of the discussion: I saw Dr. Nelson Beebe today and discovered his intent was that I bring this to the American Mathematical Society's discussion forum on Unicode, not the general one. I will be doing so, and apologize if my inquiry intruded on your work, and at the same time, appreciate the many thoughtful considerations on the matter of process of symbol standardization that I received. Best regards, Bob
