## 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!

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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)

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