Where's the Algebra?

I am told that algebra is everywhere – it’s in my iPod, beneath the spreadsheet that calculates my car payments, in every corner of my building. This idea freaks me out because I just can’t see it. I sent out a query on my blog last week asking, Who among us in the real world uses algebra? Can you explain how it works?

The first response came from an unlikely place, given my math-averse family: my brother.

Meet Brad Kagel.

Brad Kagel hangs a lighting system

He’s a rigger -- one of those crazy people who crawl up steel beams 100 feet above arenas and hangs lighting systems, sound systems and scenery for rock concerts and other shows. For years, he toured with Broadway plays and other acts. Now he owns an entertainment rigging company, based in Florida, and stages much safer corporate events and conventions.

All along, he’s had a secret life of algebra.

In the past, he said, the primary qualification for a job as an entertainment rigger was not an advanced degree in mathematics, but rather no fear of heights. These days, math skills -- as well as guts -- are important. For a job with lethal consequences, it’s not good enough to eyeball what type of truss should be used to hang a 3,000-pound lighting system, my brother says.

Algebraic formulas go into figuring out what kind of truss should be used, what type and length of wire are needed to attach lights to structural steel. Algebra is also key to keeping workers safe: It's used to calculate the shock loads that would occur if a rigger fell and were stopped in mid-air by their lanyard and harnass.

There’s typically at least one person on any given job that can do these calculations. But my brother wants all his employees to do the math, and he has been holding tutorials to review square roots and translate formulas. The goal is to get them all to pass the algebra-heavy certification exam for riggers.

But he could use some help, perhaps from some people with advanced degrees in mathematics. Here is a list of formulas that riggers are expected to know for certification (Courtesy of the Entertainment Technician Certification Program).

The ones circled in red are frequently used on the job to figure out things like "load distribution," "bridle leg tension" and "leg length." The others are more or less a mystery to Brad and his coworkers. As my brother prepares his riggers for the test, he’s wondering if any mathematicians or physicists out there can help translate.

Courtesy Brad Kagel

When might these formulas come in handy? How could they be applied to help hang a lighting system?

And don't forget to send more stories from the work place as we keep looking for algebra in unexpected places...


UPDATE: My apologies. I had planned to run a list of diagrams that riggers use that would help put these formulas in context. In the end I could not get permission from the author of the book in which they are published. Sorry to throw this up there without more clues. I'm going to send this post to a few entertainment riggers to see if we can piece together how these formulas are used.

Thanks to reader feedback for pointing out the oversight!

By Michael Alison Chandler  |  October 13, 2008; 6:00 AM ET  | Category:  Where's the Algebra?
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Can't help you with the PDF because I don't have a clue as to what the nomenclature is. An accompanying diagram could help. I see ratios and some simple rule of thumb force equations, but without knowing the use, I can't explain them.

Equations can't be used in a vacuum.

Need another use of Algebra? Ever go to the store with $10 and want to figure out how many of something you need?

$10 = (Cost of item) x (number of items)

Which means

(number of items) = $10 / (Cost of item)

That's algebra.

Posted by: kolbkl | October 13, 2008 7:54 AM | Report abuse

Unfortunately, for us to be of real help to you, we'd need more than a page with a bunch of equations with various mysterious letters and numbers and no other information.

Equations become useful when you know what all the letters/numbers stand for and their meanings within a larger system.

Once you know what all the component pieces do, you can often piece together the meaning of the whole equation.

Some of those certainly look like length or tension formulas, but I don't have any clue what their various terms are referring to.

I'm going to make some sensible guesses and say that V probably stands for a vertical length, H a horizontal one, D a depth, W a weight (maybe)...of what? Depth of what, weight of what? The page has no information.

And what do all the other letters stand for?

What does the layout of whatever these folks are building actually look like, so that we know what the weights and depths and lengths actually mean in a physical sense?

Do you understand why all of this information is crucial, and why a page of formulas with absolutely no other information is often useless?

I don't mean the following in a rude or mean-spirited way:

This is a page of equations with symbols, terms, and meanings that are used in one very specific niche of one pretty specific career.

"W" or "D" or "N" means something in particular to a rigger who is doing a calculation, and all of these equations apply to systems that a rigger would build or work with.

How is a mathematician or a physicist or an electrician, welder, biochemist, financial analyst, architect, nurse, or whoever supposed to know what any of those letters mean or how they apply to the very specific set-ups that a rigger uses?

I'm completely baffled that you would think that any old "math person" reading that page of equations would instantly know what they mean in the context of what a rigger does and exactly how they apply to the physical systems that a rigger works with.

I mean, it's not like mathematicians, nurses, and financial analysts all know what on Earth a "bridle leg" is. Can you really see a financial analyst pulling up that page of equations and being like "oh, right, clearly this is meant to calculate the distribution of loads on the bridle leg of the sixth arm of the lighting system doohickeywhatsit"?

I am puzzled, I truly don't mean any malice, and I hope you'll explain what your thought process was.

Maybe you'll get lucky and an entertainment technician will show up to explain what all of the terms in those equations stand for and what the equations are good for.

Posted by: fonkyou | October 13, 2008 8:02 AM | Report abuse

By the way, I think this blog (and your year of algebra) would be significantly improved if someone were posting alongside you who is comfortable with extensive use of math and does understand where mathematics is used in our appliances, workplace calculations, recipes, etc.

Is the teacher from whom you're taking algebra actually giving scenarios where you might see a certain form of an equation pop up, or explaining what matrices are good for, beyond "scientists use them for very complicated and useful stuff"?

Has she explained that the letter X (or W, or D) is just a placeholder, a term that is meant to stand for some quantity, and one whose meaning can change depending on the equation or model that it's used in? X might mean "number of rabbits" in one case or "probability that the Illinois soybean crop pod-setting yield in the second week of August 2011 will fall below 60%."

In physics, we use all of the Roman letters, all of the Greek letters, an occasional Hebrew one, plenty of subscripts and superscripts to distinguish one X or Y or \alpha from another, and on occasion when that hasn't been enough, I've even jokingly gotten my Chinese officemate to supply a few appropriate pictograms.

Posted by: fonkyou | October 13, 2008 8:20 AM | Report abuse

A second point to my first point. Your brother is actually using Physics. The concept of Force, mass, etc.

Algebra is a tool you need in order to get answers in physics, it's the moving around of pieces in an equation.

Imagine physics being your car, but algebra is something like the transmission.

Posted by: kolbkl | October 13, 2008 11:45 AM | Report abuse

Your question is a common one, Ms. Chandler. At the risk of oversimplifying, I will say that arithmetic is about combining numbers, and algebra is about combining variables that represent numbers.

As an example, if I need to carpet a rectangular 12'x15' room, and carpet costs $40 per square yard, the amount I have to spend is $40x12x15/9, or $800. (The reason I have to divide by 9 is that there are 9 square feet in a square yard.) However, that only tells me the cost of this particular room. For every rectangular room and every price of carpet, there would be a similar formula, but each room would have its own answer.

Now, suppose I am writing a computer program for remodelers. I have no way to know what size the users' rooms might be. Therefore, I have to allow the user to enter the numbers as variables, and I have to tell the computer how to combine the variables. I might use an expression like "PxLxW/9" to represent the formula. In this case, P is the price per square yard, and L and W represent the length and width of the room. Unlike the 40x12x15/9 formula, which only solves for one room, the formula with variables solves for any rectangular room and any price carpet.

Similarly, your brother has the ability to use general formulas expressed algebraically to solve for the specific circumstances he faces.

Therein lies the power of algebra. Instead of solving problems one at a time, as you do in basic arithmetic, you solve a whole class of problems by using variables.

Does that help?

Posted by: BradJolly | October 14, 2008 11:35 PM | Report abuse

As an Electrical Engineer, I use Algebra pretty frequently (Less than I use Powerpoint, unfortunately). I design Radios for cellular telephones, and use algebra when determining what circuit performance is needed to meet the radio level specifications. I also use calculus pretty frequently, although very simplified and application specific.

Posted by: davidbengtson | October 16, 2008 9:18 PM | Report abuse

Your question implies that something is only valuable if you can find concrete examples where it is useful. What would you say if I asked you "Where is the literature"? Few people use literature in their job, so why should we study it?

I enjoy literature, though I don't use it in my job. I do use math (algebra and up) in my job and I know how powerful and useful it is. But higher mathematics is also beautiful, finding connections between different ideas and exactly describing why certain methods work.

I like to compare the way we teach math to the way we teach music. If we made people play the musical scales over and over again for 12 years and never let them listen to great music, they would be bored and hate music. Yet this is mostly what we do in math classes.

Posted by: jpnolan | October 20, 2008 2:06 PM | Report abuse

I use algebra all day every day. I'm an R.N. working in a Recovery room. We take care of patients of all ages. I use algebra to determine the dose of medications. Vials, ampules, & syringes come with the amount of the drug on the label. For example you have 2mg/2cc. You desire to give 0.3mg. How many cc's do you give? The formula we use is desired over have equals desired over have. D = D
H = H
You give 0.3cc's. That was an easy example but the formula is great because we can use it for all types of medication dosage questions. It amazes me how quick & easy this formula makes math. We can even get a lot of the answers in our heads without writing it out.

Posted by: runner5k1956 | October 20, 2008 4:35 PM | Report abuse

An everyday example of algebra is a percentage problem. It is most easily visualized as a ratio A is to B as C is to D.
What percent of 25 is 4 ?
4:25 + x:100 (4 is to 25 as x is to 100)
or 4/25 = x/100
In a ratio, the product of the means equals the product of the extremes (cross multiply)
25x = 400
x = 400/25
x= 16%

Another very useful formula is temperature conversion.
9C = 4(F-32)
This works for Celsius to Fahrenheit or Fahrenheit to Celsius.

Posted by: Frank751 | October 20, 2008 8:39 PM | Report abuse

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