by Gérard P. Michon, Ph.D.
If you see gibberish instead of mathematical symbols (e.g., if you can't recognize Ö2 as the square root of 2) see the end of the first section below. Otherwise, the rest of this page is mostly meant to answer the questions of people who might be curious about this website itself, rather than its contents...
We recommend the three leading browsers which maintain legacy support of the Symbol font:
Internet Explorer | Mozilla Firefox | Google chrome
Numericana pages do not prevent you from enjoying your own preferred "default" font for most of the text (except in the home page and in some footnotes, captions and sidebars). For the record, Numericana was designed with the "Times New Roman" font, which is most commonly used by default. There could be a few minor problems (awkward line breaks, etc.) when other fonts are used, although we tried to anticipate many of those. Please, let us know if you find something that looks unacceptable with your own preferred font. Thanks.
For better readability, most of the Numericana text (this page is an exception) is displayed in a relatively narrow fixed-width column that would fit in a screen-width of 640 pixels. (This is the smallest width used among all the visitors we've logged so far; 98.75% of them use wider screens.) If you're currently using a really wide screen and find the long lines of this page more difficult to read than a book or a newspaper, then we've made our point.
With the reservations below, the pages at Numericana.com are designed to obey the "HTML 4.0" standard (except the home page, which is XHTML 1.0) and ought to be displayed as intended by all browsers. Tight layouts are often tested with some older browsers to cater to the needs of the largest possible audience.
To respect the most basic typographical conventions of mathematics, we had to depart from HTML 4.0 in one single respect (which is why you don't see the above W3C icon on all our pages, unfortunately). We do use the supposedly nonstandard <NOBR></NOBR> tag pair to prevent the breaking up of mathematical expressions at unacceptable locations (e.g., before an opening parenthesis) which cannot be otherwise disallowed. It's not a problem for anybody, since all the browsers we've ever tested handle this fairly gracefully.
The proper display of mathematical symbols has become more problematic. The issue was addressed in the W3C official recommendations given in Section 24.1 for the HTML 4.01 specifications (24 December 1999) now incorporated into the updated online document for HTML 4.0 specifications (originally issued on April 24, 1998). They state:
- Symbols, mathematical symbols, and Greek letters.
These characters may be represented by glyphs in the Adobe font "Symbol".
At the time, many of the newer character "entities" advocated by the same W3C recommendations were not yet supported by any browser. (Also, UNICODE characters were arguably never meant to address the specific graphical layout requirements of mathematics or anything else.) The above wording encouraged previous usage among HTML authors who had to render mathematical stuff from the "nondigital" world. This allowed them a way to comply with the new standard and start supporting it, as we did. That particular wording in the W3C recommendations was also perceived as a welcome commitment to a continued "legacy" support of the direct use of the special "Symbol" font, in spite of its strange encoding (which is repugnant to some). To this day, even the politically correct use of UNICODE provides only a superficial equivalence to Adobe's original "Symbol" glyphs (as illustrated by the below discussion about the "square root" glyph).
Many scientific pages have been using that "deprecated" direct use of the "Symbol" font (which does not disallow the use of the W3C validator). These valuable resources are unlikely to be rewritten for any reason, including allegiance to less flexible standards, including strict UNICODE content... The evolving fashion in the world of "rendering tools" (web browsers) may thus present a problem for readers, unless special attention is paid to the following recommendation(s):
Please, allow your browser to use the "Symbol" font :
This font is part of the basic set in all major delivery platforms (Windows, Mac, Linux). You must have the "Symbol" font enabled, or else you won't see the correct symbols in many mathematical expressions on the Numericana site (including some otherwise puzzling errors, where "" appears simply as "p").
- Your browser may have an option that prevents a page from requesting a specific font, even if it's available on your computer. Turn this option off. For example, with Mozilla under Linux, you must check the preference "Allow documents to use other fonts". (Thanks to Anton Sherwood for pointing this out.)
- Some versions of Firefox 3 have a bug which may wrongly disable the Symbol Font. There's a very strange way to work around this bug, which is described by Hutchinson at http://hutchinson.belmont.ma.us/tth/firefox3.html. (Thanks to Halian Vilela for pointing this out.)
Firefox Incompatibility Resolved :
For years, nobody had other practical problems with the "Symbol" font. In 2005, however, a growing number of <Numericana> readers reported difficulties with the new Firefox browser. Ultimately, a solution was found which made the problem go away (at least on the Numericana site) without requiring any action from our visitors. People who use Firefox to browse other scientific sites featuring the Symbol font may still be interested in the fixes presented below, which can be used without contacting puzzled webmasters (whom we simply urge to replace "HTML 4.01" by "HTML 4.0" in their DOCTYPE declarations). We're endebted to Dr. Thomas Fisher for prescribing this surprisingly simple cure which made our own site completely "Firefox friendly", apparently for all Firefox versions (see last entry below).
- Firefox user Maurice Starck reported success "in a few minutes, with a text editor" implementing the recommendations which Ian Hutchinson gives at symfontconfig.html and Wfonts.html.
- Dr. Thomas Fisher (Göttingen University) found out (2006-03-20) that [some versions of] Firefox under Windows resist all but the last of the above fixes, unless we change our own DOCTYPE declarations from HTML 4.01 back to HTML 4.0. in which case no fix at all is required! Although the reason for this is obscure, we are now declaring as HTML 4.0 every page that gets updated. The process should be complete by the time you read this.
Unfortunately, the problem remains for newer versions of Opera (beyond 5). We tested successfully the above "magic link" solution with Opera 9.02 (2006) so at least a modicum of legacy support exists for the symbol font even for Opera users.
We've heard many lectures by purists against that use of the "Symbol" font, now that a large set of 16-bit UNICODE characters is fairly widely available. Nevertheless, there's still a need for a firm commitment in support of the "Symbol" font across all delivery platforms, for continued use by the scientific community (no matter how repugnant this might be to some). It seems clear that browsers ought to be able to display archival online documents. Without legacy support, futures standards themselves would lack credibility at birth. The lifetimes of large sets of consistent online documents would eventually become too short to motivate their very creation (very few of them, if any, could be rewritten reliably at the rate imposed by shifting standards). For now (2006), more than 95% of Numericana visitors can still read our symbolic equations with their favorite browser (and we suspect nearly all of them could fall back on either Internet Explorer or Mozilla/Firefox if they have to).
We must point out that there's still no acceptable HTML substitute for most of the special characters of the "Symbol" font, which were designed to allow HTML typesetting of mathematical expressions over multiple lines (using TABLE capabilities). The Symbol font presents native support for extended brackets and/or integration signs spanning several lines of an equation. These things are still an incomplete afterthought in UNICODE.
Such graphical flexibility is clearly outside the scope of UNICODE. In this example, UNICODE won't provide anything other than the (virtually useless) "root-and-vinculum" combination now dubbed "√", namely: √ (i.e., UNICODE √).
Unfortunately, the issue is currently discussed only as a policy issue about new standards, without regards for the needed legacy support of many irreplaceable extant documents. To skirt the issue, some designers of scientific HTML-based documents have been forced to use screen-resolution images, which look fuzzy when printed. We use them ourselves, but only for h-bar and doublestruck symbols, for lack of a better alternative.
The first version of the Numericana home page went online in March 2000 with little or no content (a detailed history is available which tells when successive pages were actually first put online). We've since claimed "Numericana" as a trademark. Our first Guestbook was opened around that time but, predictably, attracted no attention for more than a year (it was closed 10 years later when AT&T Worldnet was discontinued).
At the time, I was planning to write a book consisting mostly of a collection of essays on numerical and other topics with a fairly large scientific glossary. I was looking for a way to provide an online companion for this book (which I am still working on, BTW) as advertised on the current homepage.
After experimenting with a few possible formats (see Wilson's Theorem or Issue Zero) I started pumping content into this site earnestly in October 2000, with the premiering of the Final Answers section (named after the signature sentence of the ABC game show "Who Wants to be a Millionaire?" then hosted by Regis Philbin). This was considered an appropriate title for a collection of "definite" answers originally given by myself to common questions asked on public forums... I haunted the first and second incarnations of the defunct "Jeeves Answerpoint" forum at Ask.com, then www.answerpool.com (with lesser assiduity as direct e-mail questions started pouring in). Replies are often given via private e-mail only (this is a free service, although donations are welcome). Therefore, the Final Answers section only includes an [arbitrary] selection of the most interesting questions I've been asked (or should have been asked). For good measure, it also features a few spinoff pages, which do not really belong: Final Punch Lines, Not-So-Final Answers, etc.
The first two actual "answers" are dated May 3, 2000. The first one (about four-dimensional hyperspheres) has been expanded since then, but the second one is still posted here in its original [terse] form.
In April 2003, I started using heraldry on the site, in the form of small (45 by 48 pixels) escutcheons displayed whenever the work of an armigerous scientist is discussed or quoted. This began with the arms of Galileo and Descartes, displayed at left. The collection has grown to include over 200 such arms which I try to use as much as possible. For good measure, a supplementary roll of arms was introduced in the first days of 2004. It was restructured in July 2004 to feature several related categories, including a Roll of Arms of Famous Explorers and a contemporary section, where you can even nominate yourself if you are (or have been) a scientist and have a coat-of-arms...
Most of the "Final Answers" items are dated [sic]. The date shown is the date when the question was posed; the answer was usually given the same day, or shortly thereafter. However, many answers may have been polished and/or expanded over time, the date of such edits is indicated only when it has some relevance. Whenever possible, the origin of a question is acknowledged (real names or "screen names" may be used) possibly via an hyperlink tied to the date. Dates appear most significant digits(s) first (ISO 8601 standard).
The initial idea was to provide definitive answers to common scientific questions which were receiving only fuzzy answers, or overly technical ones. In each answer, we tried to use whatever language level would best suit someone interested in the question to begin with. Scientific jargon was then introduced and defined as needed.
Consequently, some of our "answers" have the style of encyclopedia articles... As the Numericana collection of articles grew over the years, some people even started to refer to it as the Numericana Encyclopedia.
We try to have fun with Science like a climber has fun with mountains: Not everybody enjoys it, but there's something fullfilling about the experience, which we are trying to share here... Occasionally, we do discuss research topics or open questions. However, you need not be first on a mountaintop to enjoy the climb.A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship,
design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying,
take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
Robert A. Heinlein (1907-1988) in Time Enough For Love (1973)
If you wish to support Numericana, please use the donation paybox at left (thanks). There are so few such donations that any payment will make my day. I kept Numericana completely ad-free for more than 6 years. However, on November 21, 2006, I gave in and started displaying advertisement from Google's AdSense to help pay for the various expenses (about $1000/year) which keep Numericana afloat. My own work is not remunerated.
Through July 2002, a third-party free service monitored the origins of our visitors. We recorded and posted that in two different pages for academic and other visitors. About 1250 domain affiliations were recorded this way. This is no longer done and this time-consuming practice won't be revived, alhough we're keeping the latest [outdated] versions of these two pages online...
We're maintaining a list of backlinks [ 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 ] acknowledging the Web pages that quote us. A recent part of this list is also found at the end of our main index. (Until 19 November 2006, this index was always kept under a size of 102400 bytes so that Google would index the whole thing. It turns out that Google removed that limit around April 2005...) We're excluding only about 1% of such reciprocal links because of foul language, which we've no business pointing to.
We're no longer keeping track of the queries that are leading people to our site (as we once did, in a naive way). Here are a few that got our attention when we peeked:
- Picture of Sir William Rowan Hamilton as a baby [Google, 2004-11-05].
- How long is the unit of time known as a jiffy? [Google, 2004-11-15]
- "Degrees of freedom" humor [MSN, 2004-11-17].
- Eternity Hebrew Symbol [Google, 2004-11-16].
- Define fire in scientific terms [Google.de, 2004-11-14].
- Malo Mori Quam Foedari [Google, 2004-11-09].
- Who discovered the first n integers?
- Why did the romans use numbers?
- Scientific names of flowers in the Philippines.
- John Baez [Google, 2004-11-09].
Below is a nonexhaustive (growing) list of generic requests which we can't honor:
- I have this question, and the following list of possible answers [...]
Have your teacher contact us, if s/he can't remember the correct choice.
- I have developped this wonderful mathematical and/or physical theory, which clearly shows how everybody before me was wrong and/or stupid... Will you please tell the World?
No [ 1 | 2 | 3 ]. On the other hand, we welcome guest authors who are looking for a home for their short monographs on anything we discuss (or might discuss). We may also post (and present as "new") any submission whose validity we've been able to check for ourselves and which seems unpublished. (This is merely a way to challenge our readers to find a prior attribution. Check out a good example of this...)
- I can't formulate the question, but I bet you can't answer it.
Don't even bother to "ask", then...