Tuesday night is taco night.  Partly because we like tacos, and partly because it is an easy dinner to prepare after returning from a variety of summer activities. 

One Tuesday, I noticed something odd and was feeling particularly inquisitive so I asked Karen, "Why do we always have three different types of tortillas?" 

She replied, "Madelyn likes her quesadillas on flour tortillas.  I like the healthy (La Tortilla Factory) tortillas and the corn tortillas are for you."

"Oh..." I replied.

Karen then added, "The healthy ones are zero points."

"Zero points?  How is that possible?"

Until now, my only real interest in points was to correctly keep track of a competitive sporting event where points are awarded for some sort of display of competence (ie. goals, racing times, golf strokes, etc...)

Apparently, now you can get points for eating.  So why would you be excited about getting zero points? 

So I probed... 

What I found is that people who participate in the Weight Watchers™ program, assign points to food.  This concept can be mathematically represented in the following equation:

Fp (Fewer points) = Lw (Less Weight)

I know that Karen has followed the Weight Watchers™ program.  I also know that it works.  And since we regularly dine together, I have been unwittingly following the Weight Watchers™ program myself without fully understanding its construct.

So I probed... 

Karen was very eager to teach me.  She retrieved this contraption that can be best described as a nutritional slide rule.  It has four gradations etched into fixed and sliding positions.  The four gradations are labeled:

1.  Dietary Fiber (in grams)

2.  Calories

3.  Total Fat (in grams)

4.  Points

The slide rule functions by finding a food's fiber value and lining it up with the food's calories.  Then read the food's fat value and record the corresponding point assignment.  This logically means that there is a mathematical relationship between grams of fiber, calories, grams of fat and points.

Now I am not a nutritionist, but I did pay attention during all my schooling in Mathematics.  I remember some basic mathematical theorems. 

One of those states that in order to compare fractions, you need to find the least common multiple (LCM) and to add, subtract, multiply or divide fractions, you need to find the least common denominator (LCD).  Another theorem states that you cannot divide anything by zero.

It seemed to me that these theorems were being violated in the basic assembly of the slide rule. 

So I probed...

"If these are zero points, then you could eat the whole package and not contribute to your daily point total - right?"

"Well no, I count 1 point for two tortillas."   Karen re-butted.

"So two food items that independently calculate to zero points can result in an aggregate of one point?"

Karen gave me a look - while I will never really know, it looked like she was thinking, "You idiot! - don't question the points system!  Trust me - it just works."

...but I couldn't let it go...  So I started plugging numbers into the slide rule.  The healthy tortillas formula was:

8g (fiber) - 50 calories - 2g (fat) = 0 points!

On the healthy tortillas package, they advertised being low carb as well.  Actually 3 net carbs!  Here was the formula for carbohydrates:

11g (carbs) minus 8g (fiber) = 3g (carbs)

Now wait just a minute!  That is simply not mathematically correct!  Carbs minus fiber equals less carbs?  No, no, no!  I'll prove it using different algebraic variables:

11(x) - 8(y) = 3(x)     ...or how about this

11(houses) - 8(cars) = 3(houses)    ...or

11(miles) - 8(bananas) = 3(miles)    ...or

11(songs) - 8(weddings) = 3(songs)   ...or

11(anything) - 8(anything else) = 3(something)

So there I was, right in the middle of a mathematical conundrum (and mysteriously hungry too.)  Since it has been quite a while since I've studied math theory, I decided to do some research to try and find an explanation to the following rational problems:

Problem 1.  How can a tangible food product (tortillas), having nutritional value measured in grams of fiber, calories and grams of fat, possibly result in zero points?

Problem 2.  How can a marketing team advertise a food product as having 3 net carbs by subtracting 8 grams of fiber from 11 gross carbs?

So I probed... 

I found several possible explanations.  Since these explanations often contain complex formulas that are beyond my ability to duplicate with this blog editor, I will provide links to each one.

The At Least One solution.   "At least one" is a mathematical term meaning one or more. It is commonly used in situations where existence can be established but it is not known how to determine the total number of solutions.

This term can be illustrated in the following tale:

"There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician. And they have just crossed the border into Scotland and they see a brown cow standing in a field from the window of the train (and the cow is standing parallel to the train).

And the economist says, `Look, the cows in Scotland are brown.'

And the logician says, 'No. There are cows in Scotland of which at least one is brown.'

And the mathematician says, 'No. There is at least one cow in Scotland, of which at least one side appears to be brown.'

The Rational Zero Theorem solution.  This theorem asserts that zero can be a rational conclusion if you just create an equation from a bunch of Greek symbols and discuss it with someone who never passed calculus.

The Sextic Equation solution.  This theorem asserts that zero can be made equivalent to seven preceding factorals regardless of the value assigned to each.

The Fuzzy Logic solution.  This solution asserts that if you create a contraption (slide rule) that looks official, it will work.

The Existence Problem solution.  This is one of my favorite explanations since it asserts that if the existence of a problem is questionable, than it simply shouldn't be considered as a problem.  Karen subconsciously depended on this solution when she gave me "the look".

Abel's Irreducibility Theorem solution.  This solution asserts that Weight Watchers™ points can be reduced gradually, and anything less than one, but greater than zero should automatically be considered zero.  This gives credibility to the zero section of the Weight Watchers™ slide rule.

The Zero Polynomial Theorem solution.  This may be the best explanation for both Problems #1 and #2.  It asserts that if a polynomial uses different bases (fiber and calories), a non-educated person will accept its premise and feel good about their nutritional selections even if those nutritional selections were acquired at a price outside of the statistical normal bell curve for similar foods (designated by alpha).

So I stopped probing... 

Finally, I can sit down and eat my seven tacos smothered with cheese, sour cream and salsa.  Honey, do we have any beer?