Friday, March 19, 2010

the mass balance of cookies

Part of my time/energy the past few days has been focused upon getting things set up correctly to make Mathmatica work for mass balance calculations. Mathmatica is a powerful tool that can do amazing calculations *if* the user first sets up the data files exactly correctly, and then creates (or, more commonly, edits previously existing) files which tells it what to calculate and where to find the data files upon which to perform the calculations. Now that I’ve got it working, I thought I’d take a moment and share with you a bit about what mass balance calculations are.

Anyone who has ever decided to do lots of baking for a party understands how to look at the various recipes, make note of how much of each ingredient is needed, and then add up the totals for any ingredient which appears in more than one recipe.

Imagine that I decided to make three batches of blond brownies, 2 of oatmeal current cookies, 2 batches of vanilla cookies, and 4 batches of peanut butter cookies. Using the recipes below that would mean that all of the combined cookies would contain a total of 6 cups of oats, 14 cups of flour, 5.5 teaspoons of baking powder, 4.5 teaspoons of salt 1 cup of honey, 4 cups of brown sugar, 2.5 cups of white sugar, 6 cups of butter, 11 eggs, 6 teaspoons of vanilla, 2 cups of peanut butter, 1.5 cups of nuts, 1.5 cups of chocolate chips, 1⅓ cups of currants and 1 teaspoon of cinnamon.

Now, what if I gave you that pile of ingredients, and the recipes, but didn’t tell you how many batches of each one to make, but I did require you to follow the recipes exactly and to use up all of every single ingredient, without wasting anything.

That is what mathmatica is doing for the mass balance calculations. We tell it the starting bulk composition (the list of ingredients), and the recipes (the composition of each mineral that is present, and the list of all the minerals that are present) and ask it how much (how many batches) of each mineral can be made from those ingredients.

I don’t truly understand how it is doing it, but it uses a “monte carlo sampling” to do this. We tell it how many tries to make (100 tries takes only a few seconds) and it tries various combinations of how much of each mineral (how many batches of cookies). I think that it may be comparing the ingredients needed for each of its guesses with the list of ingredients actually present. The larger the number of tries we tell it to make (my boss suggests that it should be at least 1000), the more accurate the results will be.


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Blond Brownies

1 c. sifted flour

½ t b. powder
½ t b. soda
½ t salt
⅓ c. butter
1 c. brown sugar
1 egg
1 t vanilla
½ c. chopped nuts
½ c. chocolate chips

Sift flour, baking powder, baking soda & salt together. Add nuts and mix well.


Melt butter & add sugar and mix well. Cool. Add eggs & vanilla to butter/sugar and mix well.

Add flour mixture, a small amount at a time, mixing well after each addition. Add chocolate chips and turn into greased pan 9 x 9 x 2 (inches)

Bake at 375 for 20-25 min.
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Oatmeal Current Cookies

Put 2/3 cup of currents into a cup, and cover (just till the liquid shows at the top layer of currents) with a blend of 1/2 apple juice, 1/2 lemongrass tea, put into the microwave on full power for thirty seconds, then let stand till cool.

In one bowl mix:

3 c oats

1 c flour
1 t salt
½ t backing soda
A dash of cinnamon

In another bowl mix till light and fluffy:

1 c soft butter
½ cup light brown sugar
3/4 c raw sugar
1 egg

Add the cooled juice/currents to the butter mixture, and fold in the oat mixture. If too sticky, add a small amount more flour. Roll into 2 – 3 cm balls, place on greased paper, bake at about 180 C for 7 to 10 minutes till they are only barely golden brown. Cool on a wire rack.

Note: I used the juice/tea blend because that is what I put on my muesli in the mornings for breakfast, so I had it on hand. You could use all juice, for a sweeter result, or all tea, for a less sweet result, if you wanted.
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Vanilla cookies

½ cup butter

½ cup sugar
¼ tsp vanilla
1 egg
2 cups plain flour
1 tsp baking powder
egg or milk for glazing
pinch salt

Preheat oven to 160ºC.

Cream butter sugar and vanilla. Beat egg and add. Add sifted flour and baking powder. knead lightly. Roll out part of the mixture at a time, keeping remainder cool. Cut shapes. Put onto greased pan Glaze with a little egg or milk, dust with cinnamon or Place a piece of cherry or almond on each. Bake 10 minutes to pale gold
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Peanut butter cookies

½ cup butter
½ cup peanut butter (natural style--chunky)
1¼ cups all purpose flour
1/2 cup sugar
¼ cup honey
1 egg
½ tsp baking soda
½ tsp baking powder
½ tsp vanilla

Mix butter and peanut butter well. Add sugar. Add ½ cup of flour, honey, egg,

baking soda, baking powder and vanilla. Beat till thoroughly combined.

Beat in remaining flour.

Shape dough into 1 inch balls. Place 2 inches apart on an ungreased cookie sheet. Flatten with a fork.

Bake in oven at 375 for 7 to 9 minutes or till bottoms are lightly brown.

Cool cookies on a wire rack.
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2 comments:

Steph said...

So how many tries did Mathmatica take to get the correct number of cookie batches for your hypothetical party?

A Life Long Scholar said...

I confess that I didn't even let it try. Didn't see the point, since I'd already chosen the number of batches and calculated the necessary ingredients for that quantity of cookies.