Showing posts with label units. Show all posts
Showing posts with label units. Show all posts

Wednesday, July 30, 2014

Book Review: Realm of Measure, Isaac Asimov (1960)

Removed from circulation from my school library and regulated to the trash pile before I spotted the circa-1960 photo of Isaac Asimov on the back cover (looking younger than I've ever seen him before, so I surprised myself by recognizing him), serendipity brought Realm of Measure: From the yardstick to the Theory of Relativity into my possession.

I'm happy that it did. Though billed as an exploration of mathematics, he veers off a bit into scientific measurements, but I'll still count this toward my goal of reading one interesting book on math each summer, and this one does it without spinning out of control with endless, overly-complicated and overly-ridiculous equations.

Asimov goes into the history of measurements and how certain units came about and how the different units relate to one another. Not only did lengths like palms and feet have to be standardized from person to person and town to town, but also in relation to each so that they could be divided more evenly among people without formal education but who could count and compute the basic operations.

Asimov pushes for the metric system often throughout the book, as it's used a lot in science (where he was quite at home), not to mention in most of the non-English-speaking world. (He doesn't actually mention the measure of the English-speaking world using British units.)

The biggest problem with his arguments is that he presented the beauty of American/British system in its origins. If you were a wordsmith, you might be interested in the etymology of words, where they came from and how they came to be. You wouldn't stand for simplified spellings that are attempted from time to time. (Benjamin Franklin had a serious plan to change the language and simplify spelling, for instance.) When you read the origin of who's foot we use and who's armlength, and why a furlong is 1/8 of a mile, there is a wonder to it that goes beyond, "You see, there's this stick, and it has these two marks in it...."

Further, the system of divisions make sense. Think of the times. Think of the people and how they lived. If they split things, they likely halved them. If they had to quarter something, they halved it again. How often did someone come along with nine of his friends and need things sorted out evenly among them. And for all those divisions, 10 isn't a great number to work with: you can only divide it by 2 and 5, but not 3 nor 4. Dividing 12 by 2, 3, 4 and 6 proved more convenient, if it you lose 5. Moreover, metric conversion is easy in that you can switch units simply by moving the decimal point, but first you had to invent the decimal point! And that didn't happen to, what, the sixteenth century?

Oddly enough, I can sit here and argue that the time for the metric system has passed. We're living in a computer age, ruled by binary and hexidecimal. The number 10 really doesn't fit well into that scheme. And once you get passed 11th year math, base 10 goes out the window in favor of natural logs and e.

Not that any of this took away from my enjoyment of his book, which I heartily recommend to all with the proviso, "Don't try to read it in bed when you're really tired."

And I'll close by considering how close NYC came to allowing 16-ounce soft drinks while banning 500 milliliters. Metric: not even once.

Thursday, August 19, 2010

Google Calculator: Celsius Degrees and Square Dollars

In the past few days, I've seen images from Google calculator pop up on MathFail.com, as well as on digg, reddit and elsewhere. The image shows the following equation:

(0 degrees Celsius) + (0 degrees Celsius) = 273.15 degrees Celsius


Cut and paste the left side of the equation into Google if you don't believe it. Done? Okay.

While this might seem outrageous at first, it isn't the answer that's incorrect. It's the question. Google's calculator tried to parse it the best that it could.

Try either one of these and see what you get:

(0 degrees Celsius) + (0 Celsius degrees)
(0 Celsius degrees) + (0 Celsius degrees)


See the difference. The calculator does, too. One Celsius degree is not the same as one degree Celsius. The former is a unit of temperature; the latter is an actual temperature reading.

The first equation represents two positions on a scale. Those positions could just as well be named New York City and St. Louis. You couldn't add those two values together. However, if they had values on that scale, you could subtract them to find a displacement; i.e., how far apart they are. And the original equation could be changed to subtraction and yield a correct answer.

This brings me to a tip that I give my students, usually when reviewing percents (sales tax) and Order of Operations. I tell them that you can add dollar amounts, subtract them, or even divide them (in which case, have them notice that they lost the dollar sign and have them explain that back to me). However, if you ever find yourself multiplying two dollar amounts. Stop! You're most likely doing something wrong.

Which brings me to this graphic that I created, using Google's calculator:


What are square dollars? That's silly! Our dollars are rectangles.