[math-fun] more rants on ln, typography
Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians.
--what hogwash. "harder to say." My heart bleeds for you. First of all, lg occurs in number theory and computer science, so the idea only ln occurs in pure math is hogwash. My personal convention, which is you will note is superior to Halmos (of whose opinions, I have a low opinion), is: always use ln, except if you are trying, intentionally, to convey the idea that some formula enjoys validity REGARDLESS of the base of the logarithm, in which case use log. You also will notice this is a superior convention for the purposes of pure mathematicians. If they are too stupid to realize that, it is their problem, not mine. Second, where do these pure mathematicians get off proclaiming there should be pure math books divorced from the rest of reality? And what's wrong with striving in every way possible to make work more accessible to Joe Schmoe? Rather than striving to make it less accessible? And even the pure mathematicians, you will notice, write their numbers in base 10. (Proving their total hypocrisy.) Every time I make a log-plot, I use base-10 logs to do it, and I dunno, I guess pure mathematicians never need to plot anything because that would be too applied? And finally, re "l" looking like "1" and "|", you know what? THIS WAS A MASSIVE MISTAKE by typographers. And while in many ways I love Don Knuth, he was a total idiot when he designed his fonts making u and v look too similar, as well as this. He should have intentionally striven to make them all look different. He then introduced "\ell" in LaTeX to try to compensate for his own idiocy, but it was too little too late. But there is nothing stopping somebody from designing a font suited to mathematics, for a refreshing change. (Maybe has already happened?). Knuth's font sure wasn't it, but one could. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
The similarity between "1" and "l", and "0" and "O" was exploited by early typewriters, which typically omitted "1" and "0" on the grounds that they were redundant. Here's an excerpt from the wiki article on typewriters: Many older typewriters did not include a separate key for the numeral 1 or the exclamation point, and some even older ones also lacked the numeral zero. Typists who trained on these machines learned the habit of using the lowercase letter l ("ell") for the digit 1, and the uppercase O for the zero. A cents symbol (¢) was created by combining (over-striking) a lower case 'c' with a slash character (typing 'c', then backspace, then '/'). Similarly, the exclamation point was created by combining an apostrophe and a period.[47] These characters were omitted to simplify design and reduce manufacturing and maintenance costs; they were chosen specifically because they were "redundant" and could be recreated using other keys. I remember being somewhat horrified when I first learned of this. Tom
I also recoil in horror when I think about bloodletting. Happily this practice is largely in the past. So on to bigger and better things. When can we dispense with caps lock and overwrite mode? -----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Tom Karzes Sent: Monday, March 02, 2015 9:09 PM To: math-fun Subject: [math-fun] more rants on ln, typography The similarity between "1" and "l", and "0" and "O" was exploited by early typewriters, which typically omitted "1" and "0" on the grounds that they were redundant. Here's an excerpt from the wiki article on typewriters: Many older typewriters did not include a separate key for the numeral 1 or the exclamation point, and some even older ones also lacked the numeral zero. Typists who trained on these machines learned the habit of using the lowercase letter l ("ell") for the digit 1, and the uppercase O for the zero. A cents symbol (¢) was created by combining (over-striking) a lower case 'c' with a slash character (typing 'c', then backspace, then '/'). Similarly, the exclamation point was created by combining an apostrophe and a period.[47] These characters were omitted to simplify design and reduce manufacturing and maintenance costs; they were chosen specifically because they were "redundant" and could be recreated using other keys. I remember being somewhat horrified when I first learned of this. Tom _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
* David Wilson <davidwwilson@comcast.net> [Mar 03. 2015 08:11]:
I also recoil in horror when I think about bloodletting. Happily this practice is largely in the past.
So on to bigger and better things. When can we dispense with caps lock and overwrite mode?
Caps lock: use a screwdriver to pop that key off the keyboard (along with those "windows" et al. keys that occupy the spaces between the alt and ctrl keys). Some people map caps-lock to ctrl (IIRC old HP(?) keyboards had the key labeled "ctrl" right there). It is also possible to map that key to "nothing" (so pressing it simply has no effect). Overwrite mode: don't activate it??? Best regards, jj
[...]
When is the next date when the product of the month and date equals the year (minus 2000) ? --Dan
May third of this year. On Thu, Mar 5, 2015 at 10:23 AM, Dan Asimov <asimov@msri.org> wrote:
When is the next date when the product of the month and date equals the year (minus 2000) ?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Mike is correct, of course. I find 365 such dates in the thousand-year period from x001-x999. The first is x001-01-01. The last is x372-12-31. On Thu, Mar 5, 2015 at 10:23 AM, Dan Asimov <asimov@msri.org> wrote:
When is the next date when the product of the month and date equals the year (minus 2000) ?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I meant the thousand-year period from x000 to x999, e.g. 1000-1999. On Thu, Mar 5, 2015 at 11:33 AM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
Mike is correct, of course. I find 365 such dates in the thousand-year period from x001-x999. The first is x001-01-01. The last is x372-12-31.
On Thu, Mar 5, 2015 at 10:23 AM, Dan Asimov <asimov@msri.org> wrote:
When is the next date when the product of the month and date equals the year (minus 2000) ?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
OK, here's one that will take at least a few more seconds: Mentally solve for the positive x satisfying x^2 + log_10(2x) = 3 --Dan
x=sqrt(10)/2 On 3/5/2015 11:40 AM, Dan Asimov wrote:
OK, here's one that will take at least a few more seconds:
Mentally solve for the positive x satisfying
x^2 + log_10(2x) = 3
--Dan
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Definitely, the IBM Selectric was the best keyboard (although it was not a computer keyboard). Typing on one of those machines, with all the mechanical feedback, was an absolute delight. Typing on a computer keyboard has always felt to me like dancing with a mannequin.
These were the "Knight"/Symbolics keyboards. The best, ever.
-- -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] --
My idea of a perfect keyboard is different. I like the feel of the keys, but I would like them to be silent. So I can type late at night without disturbing anyone. -----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Tom Rokicki Sent: Thursday, March 05, 2015 4:40 PM To: math-fun Subject: Re: [math-fun] more rants on ln, typography Definitely, the IBM Selectric was the best keyboard (although it was not a computer keyboard). Typing on one of those machines, with all the mechanical feedback, was an absolute delight. Typing on a computer keyboard has always felt to me like dancing with a mannequin.
These were the "Knight"/Symbolics keyboards. The best, ever.
-- -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] -- _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
* David Wilson <davidwwilson@comcast.net> [Mar 06. 2015 07:15]:
My idea of a perfect keyboard is different. I like the feel of the keys, but I would like them to be silent. So I can type late at night without disturbing anyone.
My IBM ("Model M") keyboard is dated 1985 ("Manufactured in the United Kingdom"). It's sturdy as hell! http://www.clickykeyboards.com/index.cfm/fa/pages.main/pageID/5 Due to the very noisy click I now use a "Keytronic" keyboard that has the exact geometry of the IBM but is quieter. If I'd need to get a new keyboard I'd go to a shop and try them out, and buy the best I find (if good enough) regardless of the price.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Tom Rokicki Sent: Thursday, March 05, 2015 4:40 PM To: math-fun Subject: Re: [math-fun] more rants on ln, typography
Definitely, the IBM Selectric was the best keyboard (although it was not a computer keyboard). Typing on one of those machines, with all the mechanical feedback, was an absolute delight. Typing on a computer keyboard has always felt to me like dancing with a mannequin.
These were the "Knight"/Symbolics keyboards. The best, ever.
This one: http://xahlee.info/kbd/lisp_keyboards.html ? If so, I'll have to pitch the ZX81 one 8-)
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Those keyboard (in the original form) used hall effect switches, which I believe are now very rare. They were chosen for high reliability. As far as layout is concerned, I believe the best feature was the location of the “rubout” key immediately to the left of the A key. I still wish I could find a keyboard with that location. How else can I correct my misakes rapidly enough… We understood even back then how completely useless caps lock was, compared to virtually anything else. The arrangement of modifier keys on the lower left and right for “chording” commands was important, and has also been lost. I’m also amazed that a set of extremely useful features such as the “run bars” which take just a single pixel high at the bottom of the screen, and let you see processor, disk, and network activity have never made it into the mainstream. Also, the mouse documentation line, telling you what will happen when you click the mouse.
On Mar 5, 2015, at 9:44 AM, Henry Baker <hbaker1@pipeline.com> wrote:
These were the "Knight"/Symbolics keyboards. The best, ever.
I was able to type at 120 wpm on these keyboards.
At 07:19 AM 3/5/2015, Joerg Arndt wrote:
Some people map caps-lock to ctrl (IIRC old HP(?) keyboards had the key labeled "ctrl" right there).
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Rubout key ! I stand "corrected" ! Nowadays, we need a single-pixel-high "NSA/GCHQ/PLA bar", showing the level of activity of the various spy agency hackware currently running on this computer/smartphone. At 08:02 AM 3/6/2015, Tom Knight wrote:
As far as layout is concerned, I believe the best feature was the location of the âÂÂruboutâ key immediately to the left of the A key. I still wish I could find a keyboard with that location. How else can I correct my misakes rapidly enough We understood even back then how completely useless caps lock was, compared to virtually anything else. The arrangement of modifier keys on the lower left and right for âÂÂchordingâ commands was important, and has also been lost. IâÂÂm also amazed that a set of extremely useful features such as the âÂÂrun barsâ which take just a single pixel high at the bottom of the screen, and let you see processor, disk, and network activity have never made it into the mainstream.
We understood even back then how completely useless caps lock was,
Interesting. I remember that the SAIL keyboard had a top lock button and that I thought that was wonderful. My candidate for a ``layout'' change is to swap hypen and underscore as the upper and lower case characters on that key, coupled with a vote for using undrescore more. Whit
On 2015-03-06 08:24, Whitfield Diffie wrote:
We understood even back then how completely useless caps lock was,
Interesting. I remember that the SAIL keyboard had a top lock button and that I thought that was wonderful.
My candidate for a ``layout'' change is to swap hypen and underscore as the upper and lower case characters on that key, coupled with a vote for using undrescore more.
Whit
Those keyboards suffered a disastrous blunder--the qwerty and asdf rows obliviously repeated the http://en.wikipedia.org/wiki/Brickwork#mediaviewer/File:Brickwork_in_heading... pattern instead of slope 4/3. --rwg
* Tom Knight <tk@mit.edu> [Mar 06. 2015 19:49]:
Those keyboard (in the original form) used hall effect switches, which I believe are now very rare. They were chosen for high reliability.
They would likely be quite pricey...
[...]
I’m also amazed that a set of extremely useful features such as the “run bars” which take just a single pixel high at the bottom of the screen, and let you see processor, disk, and network activity have never made it into the mainstream.
There is xosview (and many others). OK, they use more than one pixel of height.
Also, the mouse documentation line, telling you what will happen when you click the mouse.
At least some KDE programs have a feature called "what's this?": after pressing shift-F1 you get "ballon tooltips" for any element you hover over.
[...]
Best regards, jj
On 03/03/2015 01:26, Warren D Smith wrote: [me:]
Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians.
--what hogwash. "harder to say." My heart bleeds for you.
I wasn't asking for sympathy.
First of all, lg occurs in number theory and computer science, so the idea only ln occurs in pure math is hogwash.
It's a good thing, then, that I (1) didn't say that and (2) already said in so many words that lg occurs more now than it used to.
My personal convention, which is you will note is superior to Halmos (of whose opinions, I have a low opinion),
(This distinguishes Halmos from everyone else in the world how? It must be frustrating for you, living in a world where everyone else is an idiot.)
is: always use ln, except if you are trying, intentionally, to convey the idea that some formula enjoys validity REGARDLESS of the base of the logarithm, in which case use log.
A very reasonable convention, indeed.
Second, where do these pure mathematicians get off proclaiming there should be pure math books divorced from the rest of reality?
The same place as chess players get off proclaiming that there should be books about chess divorced from the rest of reality, I suppose. Seriously, who said anything about "divorced from the rest of reality"? If you are writing a book about (say) complex analysis, then you may need a lot of natural logs and will have little use for logs to other bases. This is equally true whether or not your book mentions applications of complex analysis in fluid dynamics, electrical circuit design, analytic number theory, etc.
And what's wrong with striving in every way possible to make work more accessible to Joe Schmoe?
The same thing that's wrong with striving in every way possible to do any other single thing: you may end up making bad tradeoffs. Accessibility-to-Joe-Schmoe is good; so is conciseness, so is not confusing expert readers by using notation that Schmoe expects and they don't, etc. (Don't misunderstand me; I am *very much in favour* of making mathematical writing accessible to less-expert readers and I would love the balance to shift in that direction relative to where it is now. But accessibility doesn't always come for free and I'm not sure *anything* is so super-important that it should be striven for *in every way possible*.)
Rather than striving to make it less accessible?
I know of no reason to think that anyone does this (though for all X one can find occasional people who do X).
And even the pure mathematicians, you will notice, write their numbers in base 10. (Proving their total hypocrisy.)
Are you just trolling here? Because I find it very, very difficult to believe that someone as intelligent as you seriously thinks that writing numbers in base 10 but finding that natural logs occur vastly more often than base-10 logs in their work is evidence (still less proof) of "total hypocrisy".
Every time I make a log-plot, I use base-10 logs to do it, and I dunno, I guess pure mathematicians never need to plot anything because that would be too applied?
When you make log-plots, how often do they have actual logs in them? (In my case: never. The axes are labelled with the numbers themselves, not their logs; the only mention of logs is in an annotation saying "Scales are logarithmic" or something of the kind.)
And finally, re "l" looking like "1" and "|", you know what? THIS WAS A MASSIVE MISTAKE by typographers.
Yeah. But much of the fault belongs with the design of the Roman alphabet, which it's hard to blame any particular people for. Any typeface that looks the way readers expect is going to make l,I,1,| all look rather alike. (And any typeface that doesn't look the way readers expect is going to be distracting.) Whoever's fault it is, it is the way it is, and it's hardly reasonable to blame pure mathematicians (or anyone else who wants to work with natural logarithms) for preferring notation that works despite this deficiency in our writing system. -- g
... while in many ways I love Don Knuth, he was a total idiot when he designed his fonts making u and v look too similar, ...
I don't understand. I have attached a pdf (and the underlying low-TeXnique manuscript) with the letters u and v in roman, text italic, and math italic. They don't look any more alike to me in Computer Modern fonts than in any others.
"\ell" in LaTeX to try to compensate for his own idiocy, but it was too little too late.
I don't understand this either. Would you have made a cursive letter l the letter l in math italic? Whit
Whit, I don't think attachments make it past xmission. At least, I didn't get one. Maybe there's a URL ? --Dan
On Mar 5, 2015, at 6:56 PM, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
... while in many ways I love Don Knuth, he was a total idiot when he designed his fonts making u and v look too similar, ...
I don't understand. I have attached a pdf (and the underlying low-TeXnique manuscript) with the letters u and v in roman, text italic, and math italic. They don't look any more alike to me in Computer Modern fonts than in any others.
"\ell" in LaTeX to try to compensate for his own idiocy, but it was too little too late.
I don't understand this either. Would you have made a cursive letter l the letter l in math italic?
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CM uses nearly identical "bowls" for the bottom of the italic u and v; this contributes to a pleasing smoothness to the page layout, but the two letters are very similar. Zapf designed fonts in which the two letters contrast more. The u might have a straight lefthand side, and the v could be more rounded, or the u might be rounded, but the v would be angular. For calligraphy, I quite like the sharp angle at the bottom of a v, but when writing by hand, there are many opportunities to ameliorate the jarring angle with other visual aspects of the page layout. With typography, you have to choose the trade-offs once and for all. No matter what font you are using for math, I think it would be a good idea to avoid mixing u and v closely. There are so many other good pairings to choose from. Hilarie
As I recall from over 40 years ago when I was involved in a company (CTI) typesetting mathematics by computer (PDP-10) for many of the math-filled journals and textbooks, the lower case Greek letter nu also looked a lot like italic v. We were able to use the standard Times font family, which has a rather beautiful italic, because we were very careful about kerning. Some years later, Knuth, who seemed unaware of the finer points of typesetting, had to design his own italic fonts to be more vertical so that letters wouldn't smash into each other. On 06-Mar-15 03:53, Hilarie Orman wrote:
CM uses nearly identical "bowls" for the bottom of the italic u and v; this contributes to a pleasing smoothness to the page layout, but the two letters are very similar.
Zapf designed fonts in which the two letters contrast more. The u might have a straight lefthand side, and the v could be more rounded, or the u might be rounded, but the v would be angular.
For calligraphy, I quite like the sharp angle at the bottom of a v, but when writing by hand, there are many opportunities to ameliorate the jarring angle with other visual aspects of the page layout. With typography, you have to choose the trade-offs once and for all.
No matter what font you are using for math, I think it would be a good idea to avoid mixing u and v closely. There are so many other good pairings to choose from.
Hilarie
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participants (17)
-
Dan Asimov -
Dan Asimov -
David Wilson -
Gareth McCaughan -
Henry Baker -
Hilarie Orman -
Jeff Caldwell -
Joerg Arndt -
meekerdb -
Mike Speciner -
Mike Stay -
rwg -
Tom Karzes -
Tom Knight -
Tom Rokicki -
Warren D Smith -
Whitfield Diffie