I have one quibble. As you probably know, I am interested in mathematical typography. I see that you are not using MathJax or MathML, Why not? You don’t have mathematics, you have pictures of mathematics. All of the math, even the A’s and X’s, are little .png files. The inline math doesn’t have the proper baseline. The displayed math looks OK in my browser, but it is pixelated when you print it or enlarge it. I know you are interested in this topic as well. How have you decided to use whatever mathematical typesetting you are using?

Should I submit this, minus this question, as a comment.

I hope you and your family are well,

— Cleve

]]>What is the nearest singular matrix of [1 0; 0 1/2]? Is there an explicit formula for its computation?

]]>On the second point, componentwise perturbaton theory and componentwise condition numbers handle this. See Chapter 7 of my book “Accuracy and Stability of Numerical Algorithms”.

]]>As far as I understand, the usual way to compute the condition number for the matrix A is to take the ratio of the largest to the smallest singular value of A. How is this related to “the reciprocal of the relative distance to the nearest singular problem”?

One more question: if A is the diagonal matrix with 1 and 1e-10 on its diagonal, A’s condition number is 1e10, but the bound on cond(f,x) way overestimates the error computing the solution of Ax=b. Can you comment on whether there exists a tighter estimate of the sensitivity to perturbations?

]]>Does your function use this property? I mean the function in https://www.polyu.edu.hk/ama/profile/dfsun.

]]>Thanks for your note about the enumitem package. Very timely for my LaTeX project.

I always enjoy your posts.

Happy Isaac Newton Day!

Raúl Martinez

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]]>As you noted, some of the definitions of computer terms might not meet your expectations. While they were sent out to computer experts, those experts might be considered generalists in your field. There are also the issues of time and space: dictionaries have hard publication deadlines, and limits on the number of pages are set fairly early on. Creating a short entry that doesn’t require the reader to look up other words in the definition is often considered valuable by dictionary editors.

Because the computation team was the nearest and cheapest resource, we’d sometimes get asked to look over word choice. At the time, Collins Dictionaries was a Sun/Solaris shop and we processed and proofed most of the English and Bilingual dictionaries in a mix of shell, awk (hence the definition) and Perl scripts. Sometimes local human bias crept in: for a while there was a definition of mouse (computer) that said they operated on top of a gridded metal pad. If you used the old 3-button Mouse Systems mice that came with Sun workstations in the mid-1990s, you’ll know where that came from …

We developed a lot of check procedures for dictionaries. Not just spelling (the obvious one), but also sorting (far more subtle than you want to know about, and pretty horrid in the pre-Unicode days too) and coverage. Coverage was a really important one and was a hard requirement of the tiny Gem dictionary: every word used in the definitions had to be defined in the dictionary itself.

We typeset most of the smaller dictionaries in-house using a homegrown tool that generated PostScript. We’d previously tried to use PostScript to generate all the hyphenation, justification and page breaks, but — as a numerics person, you’ll know what’s inevitably coming next — adding up lots of small floating-point numbers of indifferent precision resulted in different line breaks (or worse, page breaks/counts) when run on different PostScript RIPs. Complex PostScript was also unpopular with the printers as it could be terribly slow on their old phototypesetting machines.

Larger dictionaries were set out-of-house. I think the CED was set in FrameMaker. Amazingly, some of the other large titles were set in troff by a small family of wizards living in Scarborough. We never quite could work out how they did some of their magic. The combined Dictionary & Thesaurus was a tough one: dictionary definitions at the top of the page, matching thesaurus definitions at the bottom. We always had the theory that they’d extended troff’s footnote mechanism to make the layout, but like all good wizards, they weren’t telling. (We tried TeX, by the way. At the time it didn’t have precise enough page size definitions for us, had the irritating habit of dropping back to bitmap fonts for seemingly random reasons and its handling of multilingual characters wasn’t up to snuff. There never was time to get it quite right before the next deadline.)

The treatment of new words was contentious when I was there. The academic dictionary tradition was to avoid new (“buzzy”) words until their usage settled. Dictionaries have to cover their costs though and Marketing loved to have the newest words so they could outdo the competition. Words of a certain time got stripped out due to finite space: “perestroika” was one that had aged out while I worked there.

I’m glad you like the paper they print on. Thin opaque dictionary paper is rather expensive (second only to the absurdly expensive bible paper, used only on a very few very pricey editions). Dictionary paper is very strong; one should be able to pick up a dictionary just by a single leaf from near the middle of the book. I don’t recommend doing this on your newest/most treasured dictionary, though!

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