## Posts tagged ‘cooking’

### Fowl Formulae for Thanksgiving

Okay, I know you’re going to find this hard to believe, but there is disagreement on the internet. And I don’t mean about some insignificant topic like gun control or taxes or health care or the value of 6 ÷ 2(1 + 2). This is big. This is important.

We’re talking turkey. Literally.

According to the British Turkey Information Service — yes, there really is such an agency — the amount of time you should cook your turkey at 375° F can be found with the following formula:

$t = \begin{cases} 20w + 70 & w < 4; \\ 20w + 90 & w \geq 4, \end{cases}$

where t is the cooking time in minutes and w is the weight of the turkey in kilograms.

If you’d rather not do the math yourself, try the British Turkey Cooking Calculator, which will not only give you the cooking time but also the defrosting time and the size of turkey to buy for a given number of servings.

By comparison, the Meat Chart provided by FoodSafety.org says that turkey should be cooked at 325° F for 30 minutes per pound.

But the cooking website allrecipes.com says that only 20 minutes per pound is sufficient if you bake the bird at 350° F.

Whereas the good folks at delish offer the following guidelines:

Cooking Times at 325° F from delish.com

which translates to the lovely formula

$t = \begin{cases} 5w + 125 & w \leq 10; \\ 15w & w = 12; \\ 7.5w + 120 & w \geq 14, \end{cases}$

but requires that you interpolate if your bird weighs an odd number of pounds. (Like 86 pounds, the world record for heaviest turkey ever raised. Even though the units digit is 6, you’d agree that 86 is an odd number of pounds for the weight of a turkey, no?)

As you might suspect, Wolfram Alpha has a more mathematically sophisticated formula:

$\displaystyle t = T \times \left( \frac{w}{20} \right)^\frac{2}{3}$

where t is the cooking time in hours, w is the weight in pounds, and T is a coefficient to account for cooking environment. For normal conditions, T = 4.5, and the equation reduces to

$\displaystyle t = 36.64w^\frac{2}{3}$

if you use minutes instead of hours for the unit of time.

But this feels a little like a math joke; below the formula, Wolfram offers the following:

using the heat equation for a spherical turkey in a 325° F oven

Falling into the wrong hands, that idea could lead to an horrendous modification of the spherical cow joke…

The turkeys at a farm were not gaining sufficient weight in the weeks leading up to Thanksgiving, so the farmer approached a local university to ask for help. A theoretical physicist was intrigued by the problem and offered his assistance. He spent several weeks at the farm, examining the turkeys and filling his notebook with equation after equation. Finally, he approached the farmer and said, “I have found a solution.”

“Oh, that’s excellent!” said the farmer.

“Yes,” said the physicist. “Unfortunately, it only works for spherical turkeys in a vacuum.”

The Wolfram formula is very similar to one suggested by physicist Pief Palofsky, who apparently dabbled in poultry when not winning the National Medal of Science.

$\displaystyle t = \frac{2}{3} w^\frac{2}{3}$

and when converted to minutes instead of hours, this becomes

$\displaystyle t = 40w^\frac{2}{3}.$

According to Turkey for the Holidays, the average weight of a turkey purchased at Thanksgiving is 15 pounds. The cooking times for a 15-pound bird, based on the formulae above, appear to have been chosen by a random number generator.

 Recommender Time (min) Temp (° F) British Turkey Information Service 226 minutes 375 Foodsafety.org 450 minutes 325 allrecipes.com 300 minutes 350 delish.com 233 minutes 325 Wolfram Alpha 223 minutes 325 Pief Palofsky 243 minutes 325

Even if you limit consideration to those who suggest a cooking temp of 325° F, the range of times still varies from just under 2¾ hours to a staggering 7½ hours. Wow.

With Thanksgiving just around the corner, where does all of this contradictory information leave us?

A number of sites on the internet claim that the only way to adequately check the doneness of a turkey is with a meat thermometer.

The folks at recipetips.com claim that a turkey can be removed when the temperature is at least 170° F for the breast and 180° F for the thigh. Yet on the very same page, they claim, “Turkey must reach an internal temperature of 185° F.”

On the other hand, the folks at the Food Lab claim a turkey can be safely removed when the breast temperature reaches 150° F, because after resting 15‑20 minutes before carving, the amount of remaining bacteria will be minimal. They explain, “What the USDA is really looking for is a 7.0 log10 relative reduction in bacteria,” particularly Salmonella, which means that only 1 out of every 10,000,000 bacteria that were on the turkey to start with will survive the cooking process. And according to the USDA guidelines, a turkey that maintains a temperature above 150° F for 3.8 minutes or longer will reach that threshold for safety.

Which has to make you wonder — if 3.8 minutes at 150° F is supposedly adequate, why then does the USDA Food Safety and Inspection Service recommend that the minimum internal temperature of the turkey in the thigh, wing, and breast should be at least 165° F? Who knows. I suspect it’s typical government over-engineering to remove all doubt.

So, how long should you cook your turkey? Hard to say. But if you put your turkey in the oven right now, it should be done by November 23.

When the turkey is finally ready, here are a few math jokes you can tell around the Thanksgiving table.

What do math teachers do on Thanksgiving?
Count their blessings!

What does a math teacher serve for dessert on Thanksgiving?
Pumpkin Pi.

How do you keep private messages secure on Thanksgiving?
Public turkey cryptography.

Thanksgiving dinners take 18 hours to prepare. They are consumed in 12 minutes. Halftimes take 12 minutes. This is not coincidence.
~ Erma Bombeck

Gobble, gobble!

### Are Fractions Useless, or Are Americans Just Stupid?

I don’t know how else to say it, so I’m just gonna say it.

Fractions are full of sh*t.

Okay, not really. But if I have to hear one more time about how fractions are useful because of applications to cooking, I may commit hari-kari.

Before I jump into a diatribe, though, I absolutely have to share this improper fraction cartoon from Fat Rooster Studios (warning: rated PG-13).

It’s really hard to continue after that. But I’m gonna try.

There are three reasons that fractions are not really important in cooking.

• First, fractions only appear important because Americans are stupid. We insist on using the imperial system, and we measure dry ingredients in fractional parts of a cup. In other parts of the world, they don’t add 1 3/4 cups of flour to their recipe for croissants. Instead, they use 450 ml of flour. So making a half, a third, or a double recipe doesn’t involve operations with fractions.
• Second, ratios are important when cooking, not fractions. The exact amount of flour, sugar and baking powder in your chocolate chip cookies isn’t critical, so long as the ratio is 96 : 48 : 1. Approximately. Cooking is not an exact science. If your ratio of flour : sugar : baking powder = 98 : 45 : 2, you should still end up with a tasty dessert.
• Third — and, in my opinion, most importantly — great cooking derives from experience and approximation, not from exact measurements. My mother used to drive me crazy when she’d state, “But I followed the recipe,” if her normally fantastic lasagna came out less than fantastic.

Don’t believe me? Then watch the chef on a cattle drive as he makes chili over an open fire, and notice how he throws in a bucket of beans, two buckets of tomato sauce, and as much ground beef as he thinks is appropriate. You can bet your ass that Cookie ain’t got no measuring cups in the back of the chuck wagon. Or better yet, watch him make a cup of “six shooter coffee,” where his recipe is one handful of ground beans per cup of water. How much coffee is in a handful? Depends on the hand.

Maybe you think it’s just cowboys who estimate. Nope. Watch Emeril Lagasse as he adds a pinch of this, a dash of that, and — BAM! — the result is a grilled pork chop for which tourists pay \$30 when they visit New Orleans.

If you need proof that ratios are the key mathematical element to successful cooking, listen to Dr. Mark Hadley. He claims that perfect ravioli is obtained when the ratio of pasta : filling : sauce = 45 : 45 : 10, which includes just enough olive oil “to give a thin layer of 200 microns over the surface of all the pasta – enough to make it glisten, resulting in the perfect mouthful.”

But, you know what? We shouldn’t let reality get in the way of a good story. Let’s please continue to perpetuate the myth that fractions are important — nay, critical — by including exorbitant numbers of cooking problems in the fraction units of textbooks. As far as I can surmise, the majority of fraction problem authors have never actually cooked. Here’s a typical problem:

The following recipe for Blueberry Bubble Loaf makes 12 servings.

• 2 cups cereal that contains blueberries
• 1 cup brown sugar
• 1/2 cup butter
• 2 packages of refrigerated buttermilk biscuits

Rewrite the recipe so that it makes 4 servings.

Let’s assume that this isn’t stupid. (Though it is, right? I mean, it might be reasonable to make 6 servings, since that would require just one package of refrigerated buttermilk biscuits. But to make just 4 servings? That means you’ll only need 2/3 package of refrigerated biscuits. What are you supposed to do with the other 1/3 of the package?)

But as presented, the solution requires that each ingredient be divided by 3. That gives 2/3 cup cereal, 1/3 cup brown sugar, 1/6 cup butter, and the aforementioned 2/3 package of refrigerated buttermilk biscuits. I decided to make this recipe.

• I have a 1/3-cup measure in my cooking drawer, so the first two ingredients were no problem.
• I don’t have a 1/6-cup measure. I could have measured 1/3 cup of butter and used an educated guess to divide the amount in half. Instead, I can just filled a 1/4-cup measure, and decided that that was close enough. Good enough for government work.
• I’ll only need 6 2/3 of the 10 biscuits that come in a 12-ounce container of refrigerated buttermilk biscuits. WTF? I decided that 7 biscuits is close enough, and I gave 3 uncooked biscuits to my dog. He’s happy at this development. I hope he doesn’t get worms.

I cooked the blueberry bubble loaf as directed, and it came out fine. Except that the total mixture only filled 1/3 of a bread pan, and it created a loaf that was only one inch tall. That’s not a loaf; that’s a tortilla.

But generally speaking, there was no material difference between the original loaf and my reduced-height loaf, despite the imprecision in my measurements. And do you know why there was no difference?

Because fractions are full of sh*t.

Now check this out. The following is a cake recipe from About.com.

• 2 cups cake flour
• 2 teaspoons baking powder
• 1/2 teaspoon salt
• 1/2 cup butter, softened
• 1 cup sugar
• 3 large eggs
• 2 teaspoons vanilla
• 3/4 cup milk

And here’s a vanilla cake recipe from Country Living.

• 1 1/2 cups cake flour
• 1 1/2 teaspoons baking powder
• 1/4 teaspoon salt
• 1/2 cup butter, softened
• 1 cup sugar
• 2 large eggs
• 1/2 teaspoon vanilla
• 1/2 cup milk

The second recipe requires 3/4 as much flour as the first recipe. If fractions really mattered, then every ingredient in the second recipe should have an amount that is 3/4 as much as the first recipe. But they don’t. There is 1/2 as much salt, the same amount of butter, the same amount of sugar, 2/3 as many eggs, 1/4 as much vanilla, and 2/3 as much milk.

So I’ll say it again.

Fractions are full of sh*t.

At least when it comes to cooking.

Fractions are, however, fodder for some great jokes.

Five out of four Americans have trouble with fractions.

Sex has a lot in common with fractions.
It’s improper for the larger one to be on top.

It’s hard to tell the difference between a numerator and a denominator. There is a fine line between them.

Two-thirds of Americans have trouble with fractions. The other half can handle them just fine.

Son: Can you help me find the lowest common denominator of 1/2 and 1/3?
Dad: You mean they still haven’t found it? They were looking for that when I was a kid!

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

## MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.