The Orthography of Equations

Every now and then this little image appears on my Facebook page, as a sponsored ad, with the headline “Become a Physics Teacher”. The sponsors claim that they will help me get a master’s degree online in education so that I can become a physics teacher.

Now tell me, if you were considering paying someone to help you get certified in, say, programming C++, how would you respond if the image in their add had this programming fragment:

i = i + 1;

I don’t know that the above is a very clear analogy to any of you, but the point is this: if the ad in question displays a lack of knowledge of the idioms of the discipline, should you trust the advertiser to provide what’s on offer in a reliable way?

Why do I object to this little image? May I see a show of hands from the physical scientists who know the answer please?

Yes, that’s right. In this most famous equation from physics, a result of Einstein’s Special Theory of Relativity, the letters ‘m’, representing mass, and ‘c’, representing the speed of light in vacuum, are never, ever written as upper-case letters; they are always, invariably written in lower case. I should, perhaps, be more grateful that the ’2′ is at least written as a superscript.

A tiny detail, a nit that I’m picking? Would you trust a brain surgeon with dirty fingernails? A car mechanic who’s not aware of what a “spark plug” is called?

Long ago I started to draft a blog entry called “On the Orthography of Equations”, but I never got around to it. It was going to relate a story and draw some interesting conclusions.

The events of the story happened, now, some 20 years ago. I was talking to a secretary in our University department who was typing (yes, on a typewriter) a paper for another faculty member. She asked for some advice on how to type an equation. While I was answering her question I mentioned that if she put some space between two symbols and moved another to a slightly different place that the equation would be significantly easier to read.

“Easier to read?” she exclaimed. Clearly the idea that equations were somehow “read” rather than merely looked at surprised her. And that was when I realized that, to this secretary and likely to most people with relatively little mathematical training, the symbols in equation were mostly decorative and they did not realize that how the symbols are deployed affect the meaning and readability of the equations.

I was nearly as surprised as she to discover this, although it’s an observation I’ve never yet figured out what to do with. Neither am I sure that this was the blog post that I was going to write, but there you go–it’s the one you got.

Heat to Sound to Electricity

From a recent Physics News Update comes this half-science, half-technology report about a device that uses heat to make electricity, with sound as an intermediary.

The story is interesting enough by itself, but it is also a useful illustration that sometimes there are new ideas in science and technology that are not as inscrutable as general relativity or string theory, but are nevertheless pretty startling and understandable.

There’s really nothing in this report that requires much in the way of deep technical or scientific understanding, although it might help if I describe the idea of the piezoelectric effect a little. There are some substances, largely ceramics but also some naturally occurring crystals that exhibit this property: applying stress to them (e.g., squeezing them) creates an electrostatic charge, i.e., a voltage across the crystal. Sometimes this property is used in reverse: put a voltage across a piezoelectric substance and it expands by a tiny amount. Piezoelectric devices are often used, therefore, to make precision actuators, devices that move things closer together or further apart depending on an applied voltage.

TURNING HEAT INTO ELECTRICITY THROUGH SOUND has been demonstrated by the University of Utah group of physicist Orest Symko. The group has built devices that can create electricity from the heat that would otherwise be wasted in objects such as computer chips. The devices might potentially make extra electricity from the heat of nuclear power plant towers, or remove extra heat from military electronics.

At last week’s meeting of the Acoustical Society of America in Salt Lake City, five of Symko’s students demonstrated the latest versions of the devices, which they have been developing for a few years. The devices first convert heat into sound, and then sound waves into electricity. Typically, each device is a palm-sized cylinder containing a stack of materials such as plastic or metal or fiberglass. Applying a heat source, such as a blowtorch, to one end of the stack creates a movement of air which then travels down the cylindrical tube. This warm, moving air sets up a sound wave in the tube, similar to the way in which blowing air into a flute creates sound. The pitch, or frequency, of the sound wave depends on the dimensions of the tube; current designs blast audible sound, but smaller devices would create ultrasound. The sound wave then strikes a piezoelectric crystal, a commercially available material that converts sound into electricity when the sound waves put pressure on the crystal.

Symko says a ballpark range of 10-25% of the heat gets converted into sound in typical situations. The piezoelectric crystals then convert about 80-90% of the sound energy into electrical energy. Symko expects the devices to be used in real-world applications within two years, and may provide a better alternative to photovoltaic solar cells in some situations. (Session 5aPA at meeting; also see University of Utah press release at http://www.unews.utah.edu/p/?r=053007-1)

[Phillip F. Schewe and Ben Stein, Physics News Update: The American Institute of Physics Bulletin of Physics News, Number 828, 13 June 2007.]

Non-Hostile Casualties

Is it just me? I find the following paragraph very odd and unsettling. Thanks to a mention at the Whiskey Bar, we read this

(AP) — As of Saturday, April 2, 2005, at least 1,533 members of the U.S. military have died since the beginning of the Iraq war in March 2003, according to an Associated Press count. At least 1,162 died as a result of hostile action, according to the Defense Department. The figures include four military civilians.

The number 1,533 is upsetting enough as it is. But it’s the figure between the lines that catches my attention (in rather the same way that sometimes it’s worth remembering that foods that trumpet “90% fat free” are still 10% fat).
The implication of these figures is that 371 troops have died in the war not as a result of hostile action. Put another way, that’s nearly 25% of our war casualties that are not the result of “hostile action”!
What does this mean? What would be the “not hostile action” here, and what is it about non hostility that kills so many troops?

Key-Word-Based Science

I was reading an interesting article at Science Blog, “Changes in Earth’s tilt control when glacial cycles end“, about a new report (written by “Peter Huybers, a postdoctoral fellow in the WHOI Geology and Geophysics Department, and coauthor Carl Wunsch of MIT”) suggesting that changes in the tilt of the earth’s axis may indeed be the cause of periods of glaciation and other large-scale climate changes. Fascinating stuff, but not what this post is about.
This post is about the advertising. There’s a box on the page that has links provided by amazon.com, evidently chosen by matching subject key words, which in this case must have included “climate” and “warming”. At least when I loaded the page, they suggest two items:

1. A book called Global Warming, by John Houghton, and
2. A Panasonic, window model, 5,200-BTU air conditioner

Rather in poor taste, I thought, and showing a keen insensitivity to the second law of thermodynamics, not to mention several of the probable causes of global warming all represented by one device (that would be the air conditioner, not the book).
Were they suggesting that better air conditioning might be a tonic that would reduce the problem of global warming? The idea puts me in mind of all those people who don’t yet understand (we’ll get to it sometime, folks) why you can’t cool the apartment by leaving the refrigerator door open. Which, by the way, is significantly different from the reason why you shouldn’t heat the apartment by running the gas oven. Oddly, though, you could heat the house by leaving the refrigerator door open, but it would not be very efficient.

Rock into Rocket Scientist

My new motto: I evolved from a rock into a rocket scientist.

Evolutionists may need billions of years to make people believe a rock can turn into a rocket scientist, but that time just isn’t available.

[Kent Hovind, aka "Dr. Dino", from Universe Is Not "Billions of Years" Old, to be found on his "Creation Science Evangelism" website.]

Identity Theft

The problem of identity theft, a topic newly current after revelations about ChoicePoint and a “breach of security”, was the subject of dueling opinion pieces today in USA Today.
First, a few excerpts from the editorial piece that sets the context and says something that I think is a little more complicated than the editors seem to think:

The company is a data broker that boasts a collection of 17 billion public records. The records span everything from birth dates and addresses to driver’s license and Social Security numbers — just enough information to cause trouble if it gets into the wrong hands.
And it did.
The company, duped by criminals masquerading as business owners, gave up personal information on 145,000 people last year. For months, as police investigated, the consumer-victims weren’t told.

Thus, we have a company in the business of collecting “personal information” and then selling it; other companies are convinced that they must have this information to be competitive.
The editors say it in so many words, but don’t recognize this basic problem: how can one distinguish the “criminals” from the [legitimate] “business owners”? What happens when they are the same?
My point would be that, to the company selling the data, there is no real difference. What does it mean to “masquerade” as a legitimate business, and how is it operationally any different from “real” businesses?
The root of the problem, and the source of the solution, is not with enhancing safeguards on the data, since potential clients and potential thieves are indistinguishable. Either the data must not be collected in the first place — that battle was probably lost in the past decade or more — or it must be made somehow less useful to “masquerading bussinesses”.
In a response Fred H. Cate says:

A California law requiring businesses to notify consumers when the security of their personal data is breached is a poor substitute for real action to address the scourge of identity theft.
[...]
The problem at the heart of most identity theft isn’t access to information or consumer inattention, it is the lack of will and effective tools to verify the identity of consumers, especially when granting credit.

Mr. Cate certainly recognizes that the problem is not going to lie with enhancing “safeguards” on the data, nor with giving consumers notice of “security breaches”. (Talk about refusing to take responsibility by doing nothing that superficially appears to be doing something.)
When I was young and first got my own Social Security number, we were taught things about the number’s proper use that were thought to be so important and so inviolable that it might have been written in the consititution: your Social Security number is not a universal identity number, and you should NEVER allow it to be used as one.
Whatever happened to that admonition? Look how steadily it has eroded in the past 30 years until the Social Security number has become, de facto, a universal (US) ID number. For no good reason either: in most cases I can think of, it was used merely as a convenience for whomever was requesting it so that they could assign a unique number to someone for some temporary purpose. There are other ways to accomplish that, even easy ones, that don’t compromise the Social Security number.
Now, one almost never thinks about such a request, and one’s Social Security number can be found lying around everywhere. It would be simplistic to suggest that this is the sole cause of the problem and that restricting its use would halt the problem, but it is nearer the source of the problem, and looking there could lead to — if not solutions — at least mitigating strategies.
[Update, 1 March 2005:] The Detroit News offers its opinion in the editorial “U.S. Should Limit Use of Social Security Numbers”, identifying at least one of the problems that I mentioned. Whether their solution is more than just a start will require quite a bit more reflection.