Probability resources

Each Wednesday I post a list of notes on some topic. This week it’s probability.

See also posts tagged probability and statistics and the Twitter account ProbFact.

Last week: Python resources

Next week: Regular expression resources

Photo review

Here are some of the photos I took on my travels last year.

Bicycles on the Google campus in Mountainview, California:
Google bicycles

Sunrise at Isle Vista, California:

View from University of California Santa Barbara:

Reflection of the Space Needle in the EMP museum in Seattle, Washington:

Paradise Falls, Thousand Oaks, California:

Bed and breakfast in Geldermalsen, The Netherlands:

Amsterdam, The Netherlands:

Chinatown in San Francisco, California

Heidelberg, Germany

Bringing back Coltrane

In the novel Chasing Shadows the bad guys have built a time machine named Magog.

“The bottom line is this. And it is hard for me to believe. They are going to use Magog to bring someone back from the past.”

Jack did not blink or move. His heart was beating very quickly now, but he merely said wryly, “Yes? Who are they going to bring back? Tell me it is John Coltrane.”

“You are never really serious are you?”

“I’m very serious about my music. Why are bad guys always bringing back people that everyone was glad to see go the first time? We could use more Coltrane …”

Related post: Nunc dimittis

Thou, thee, you, and ye

Ever wonder what the rules were for when to use thou, thee, ye, or you in Shakespeare or the King James Bible?

For example, the inscription on front of the Main Building at The University of Texas says

Ye shall know the truth and the truth shall make you free.

Why ye at the beginning and you at the end?

The latest episode of The History of English Podcast explains what the rules were and how they came to be. Regarding the UT inscription, ye was the subject form of the second person plural and you was the object form. Eventually you became used for subject and object, singular and plural.

The singular subject form was thou and the singular object form was thee. For example, the opening lines of Shakespeare’s Sonnet 18:

Shall I compare thee to a summer’s day?
Thou art more lovely and more temperate.

Originally the singular forms were intimate and the plural forms were formal. Only later did thee and thou take on an air of reverence or formality.

Notes on HTML, XML, TeX, and Unicode

This week’s resource post: some notes on typesetting, Unicode, etc.

See also blog posts tagged LaTeX, HTML, and Unicode and the Twitter account TeXtip.

Last week: C++ resources

Next week: Special functions

Why assign two characters to the same symbol?

Unicode often counts the same symbol (glyph) as two or more different characters. For example, Ω is U+03A9 when it represents the Greek letter omega and U+2126 when it represents Ohms, the unit of electrical resistance. Similarly, M is U+004D when it’s used as a Latin letter but U+216F when it’s used as the Roman numeral for 1,000.

The purpose of such distinctions is to capture semantic differences. One example of how this could be useful is increased accessibility. A text-to-speech reader should pronounce things the same way people do. When such software sees “a 25 Ω resistor” it should say “a twenty five Ohm resistor” and not “a twenty five uppercase omega resistor,” just as a person would. [1]

Making text more accessible to the blind helps everyone else as well. For example, it makes the text more accessible to search engines as well. As Elliotte Rusty Harold points out in Refactoring HTML:

Wheelchair ramps are far more commonly used by parents with strollers, students with bicycles, and delivery people with hand trucks than they are by people in wheelchairs. When properly done, increasing accessibility for the disabled increases accessibility for everyone.

However, there are practical limits to how many semantic distinctions Unicode can make without becoming impossibly large, and so the standard is full of compromises. It can be quite difficult to decide when two uses of the same glyph should correspond to separate characters, and no standard could satisfy everyone.


[1] Someone may discover that when I wrote “a 25 Ω resistor” above, I actually used an Omega  (Ω, U+03A9) rather than an Ohm character (Ω, U+2126). That’s because font support for Unicode is disappointing. If I had used the technically correct Ohm character, some people would not be able to see it.  Ironically, this would make the text less accessible.

On my Android phone, I can see Ω (Ohm) but I cannot see Ⅿ (Roman numeral M) because the installed fonts have a glyph for the former but not the latter.


This post first appeared on Symbolism, a blog that I’ve now shut down.

Updating blog posts

I’ve been going through my old blog posts and fixing a few problems. I found a few missing images, code samples that had lost their indentation, etc. Most of the errors have been my fault, but some were due to bugs in plug-ins.

If you see any problems with a post, please let me know. You could send me an email, or leave a comment on the post. (For a while I had comments automatically turn off on older posts, but I’ve disabled that. Now you can comment on any post.)

For the first couple years, this blog didn’t have many readers, and so not many people pointed out my errors. Now that there are more readers, I find out about errors more quickly. But I’ve found some egregious errors in some of the older posts.

Thanks for your contribution to this blog. I’ve been writing here for almost seven years, and I’ve benefited greatly from your input.

What do you mean by can’t?

You can’t subtract 4 from 3 (and stay inside the natural numbers, but you can inside the integers).

You can’t divide 3 by 4 (inside the ring of integers, but you can inside the rational numbers).

You can’t take the square root of a negative number (in the real numbers, but in the complex numbers you can, once you pick a branch of the square root function).

You can’t divide by zero (in the field of real numbers, but you may be able to do something that could informally be referred to as dividing by zero, depending on the context, by reformulating your statement, often in terms of limits).

When people say a thing cannot be done, they may mean it cannot be done in some assumed context. They may mean that the thing is difficult, and assume that the listener is sophisticated enough to interpret their answer as hyperbole. Maybe they mean that they don’t know how to do it and presume it can’t be done.

When you hear that something can’t be done, it’s worth pressing to find out in what sense it can’t be done.

Related post: How to differentiate a non-differentiable function

Optimism can be discouraging

Here’s an internal dialog I’ve had several times.

“What will happen when you’re done with this project?”

“I don’t know. Maybe not much. Maybe great things.”

“How great? What’s the best outcome you could reasonably expect?”

“Hmm …  Not that great. Maybe I should be doing something else.”

It’s a little paradoxical to think that asking an optimistic question — What’s the best thing that could happen? — could discourage us from continuing to work on a project, but it’s not too hard to see why this is so. As long as the outcome is unexamined, we can implicitly exaggerate the upside potential. When we look closer, reality may come shining through.

 Related posts:

Titles better than their books

What got you here won’t get you there. I’ve been thinking about that title lately. Some things that used to be the best use of my time no longer are.

I bought Marshall Goldsmith’s book by that title shortly after it came out in 2007. As much as I liked the title, I was disappointed by the content and didn’t finish it. I don’t remember much about it, only that it wasn’t what I expected. Maybe it’s a good book — I’ve heard people say they like it — but it wasn’t a good book for me at the time.


I’ve written before about The Medici Effect, a promising title that didn’t live up to expectations.


“Standardized Minds” is a great book title. I haven’t read the book; I just caught a glimpse of the cover somewhere. Maybe it lives up to its title, but the title says so much.

There is a book by Peter Sacks Standardized Minds: The High Price Of America’s Testing Culture And What We Can Do To Change It. Maybe that’s the book I saw, though it’s possible that someone else wrote a book by the same title. I can’t say whether I recommend the book or not since I haven’t read it, but I like the title.


I started to look for more examples of books that didn’t live up to their titles by browsing my bookshelves. But I quickly gave up on that when I realized these are exactly the kinds of books I get rid of.

What are some books with great titles but disappointing content?

Public reaction to Ebola

Ebola elicits two kinds of reactions in the US. Some think we are in imminent danger of an Ebola epidemic. Others think Ebola poses absolutely zero danger and that those who think otherwise are kooks.

Nothing can be discussed rationally. Even narrow scientific questions lead to emotionally-charged political arguments. Those who have a different opinion must be maligned.

The big question is whether the Ebola virus can spread by air. Experts say “probably not” but some are cautious. For example, Ebola researcher C. J. Peters says “We just don’t have the data to exclude it.” But people who know absolutely nothing about virology are firmly convinced one way or the other.