Clegg's Grand Unification Theory of Delivered Pizza: The Math Behind the Pizza

TROY, New York -- In His continuing research on pizza, Kahuna has unearthed Paul Clegg's Grand Unification Theory of Delivered Pizza originally published here in the Project Galactic Guide, August AD 1994.

While Paul Clegg is more commonly known for his work with Project Galactic Guide, what is not so commonly known is his work with the Grand Unification Theory.

The Grand Unification Theory, that is, of Delivered Pizza.

One particularly boring weekend, while gaming with some friends in the basement of one of Rensselaer Polytechnic Institute's lecture halls, one of Paul's friends had some pizza delivered. Upon receipt of the pizza, which was, apparently, on time but late as usual, Paul noted their response to the temperature of the pizza.

"It's not very hot," they said. Almost immediately, the clockworkings of Paul's brain, dusty though they were, set into motion, pondering the mathematics behind the delivered pizza.

"Is it any good?" Paul asked. And in reply, his friend, with a mouth full of not-quite-hot pizza, mumbled an unexcited affirmation.

Paul then thought that perhaps the quality of a pizza was somehow related to the temperature of the pizza. He also then theorized that the warmth of the pizza was, of course, indirectly proportional to the time it took for the pizza to arrive.

This set down the framework for one of the basic principles and formulas for determining the quality of a delivered pizza. In recognition for his brilliant discoveries in the field of Pizza Delivery Mathematics, the entire team of researchers working in the field named the unit of measure for pizza quality the "Clegg." Eventually, the quality equation was filled out to a more robust form, as shown below:

                             P T

                       Q = -------

                           t (1+I)

Q is the quality of the pizza, measured in Cleggs, and represents the unit dollars Kelvin per minute. T is, of course, the temperature of the pizza upon delivery, and is measured in Kelvins. P is the price of the pizza, in American dollars. t is the time taken for the pizza to be delivered, in minutes, starting from the end of the phone call, to the point at which the box of pizza is opened at the receiving end.

I is a slightly odd concept. It measures the "Italianicity" of the name of the establishment from which the pizza was ordered. I takes on a value of arbitrary value, based on how "Italian" the name of the pizza joint has. So whereas Domino's Pizza scores only a 0.2, a place called Italia's is upwards of a 0.8. The scale only operates between 0 and 1, and the scale has been named "The Toigo Scale," in honor of the man who added it to the equation, Mark Toigo, a chemical engineer at RPI. To receive a scale of 0, the pizza parlor's name would have to be something like "Billy Bob's Pizza," and written in Sanskrit.

An average Domino's Pizza Large has been found to score about 118.10 Cleggs, with a price of about $12.80, an arrival temperature of about 310 Kelvin, a delivery time of about 28 minutes, and rating a 0.2 on the Toigo Scale.

Amazed with this initial discovery, Paul and his compatriots, who may, or may not, have included Mark Toigo, Sam Blue, Deb Atwood, Kevin Allen, Shawn Havranek, Nigel Westlake, and Brian Moore, set out to derive some more mathematical truths behind delivered pizza. What you'll find below is a somewhat disjointed collection of the more important findings made on that glorious night.

1. The time t required to receive a pizza is inversely proportional to the distance D from your location to the pizza joint. Thus, we introduce a proportionality constant, Beta, and end up with the following equation:

             Beta

         t = ----

              D



         Where Beta is a constant in m * s.

2. The lifetime of a pizza parlor is equal to the average price of their pizza P(avg), times the average temperature of the delivered pizza T(avg) in Kelvin, times a constant Alpha, divided by the average quality of their pizza Q(avg):

                      P(avg) T(avg) Alpha

          lifetime = ---------------------

                             Q(avg)

Check the units. They work out.

3. The ability to taste a topping on a pizza is inversely proportional to the number of toppings on the pizza.

4. Shawn's Law: The size of an individual topping element is inversely proportional to the price of the pizza.

5. The quality of a pizza approaches zero (Q -> 0) and the amount of cheese found on the pizza approaches zero, as the number of toppings approaches infinity.

6. The frictional coefficient of a pizza's cheese is equal to a constant divided by the quantity of sauce. The coefficient is measured in "Debs," and R_c is the "Deb Constant."

                                    R

                                     c

                         f       = -----

                          cheese   sauce

7. The thickness of cheese may be determined by the following computation:

            (sum(leftturns)-sum(rightturns)mv

thickness = ----------------------------------

                     f       m       a    R

                      cheese  cheese  car

8. The likeliness of a delivery person finding your location is inversely proportional to the simplicity of your address or directions. Thus, if you are standing inside the pizza parlor itself, chances are slim that the delivery person will actually find you. This is not to say that overly complex instruction sets will improve the chances greatly.

9. The Blue Effect: The time it takes a Domino's Pizza delivery person to deliver a pizza is inversely proportional to the number of police cars patrolling the route taken by the driver.

9a. Corollary to the Blue Effect: A Domino's Pizza delivery person will always deliver a pizza faster than the average police response time.

9b. Corollary to the Corollary: The average police response time is much much much greater than the response time of a Troy Ambulance.

10. The IQ of the pizza driver, and the IQ of the person who takes the order at the pizza shop, sum to a constant. This constant has been approximated to about 120.

11. The time required to come to a decision on what toppings to order is equal to the exponential of the square of the number of people trying to decide. If n is the number of people, the time, in minutes, is equal to:

                        2

                       n

                      e

12. The time in which a pizza is consumed is equal to the number of people who paid for the pizza divided by the number of people who actually ate some of the pizza, multiplied by a time constant.

Note that these formulas can only apply to delivered pizza. Frozen pizza, homemade pizza, and take-out pizza are forms of pizza that may not subscribe to these natural laws.

There, it's a lot clearer now.