How Handmade Noodles and Calculus Are The Same
Much of the complaining about math that I have heard over the years goes like “I’ll never use this in real life.”
I beg to differ.
I was winding down after my work day, sitting at the computer and trying to decide whether playing solitaire was more desirable than looking over sports scores. Delicious scents were wafting from the general direction of the kitchen. I then heard a gentle but insistent summons for my presence. From the kitchen.
Now, my presence in the kitchen is chiefly in the form of hovering. My girlfriend is a talented cook, and my experience in that direction has mostly been as a competent but “subsistence” level chef. Most of the time she just shoos me away when I hover.
Sometimes, she enlists my acceptable sous-skills to peel potatoes, slice veggies, or stir something that requires attendance but not actual attention. Infrequently, she asks me to do something that calls for a little dexterity and a large capacity for following directions.
This was one of those latter occasions.
In our household, the final use of a leftover rotisserie chicken from a “big box” store is soup stock. In this particular case, the eventual goal was chicken noodle soup. She had spent time cooking down the chicken carcass along with carrot tops, celery bottoms, onion ends and various seasonings and other yummy stuff. While all these tailing were simmering together, she mixed the necessary ingredients to make noodle dough. Noodle dough, I’m told, is very full of gluten. That means that when you roll it out, it tends to “snap back” due to the stretchiness. I even know what I’m talking about here…I’ve watched the Great British Bake-Off.
At some point she realized that rolling out the dough was something she could delegate to someone with pedestrian but reliable skills. This is where I came in.
Most dough-rolling I had done in the past was for pie crust. When you roll, it stays put. I’ve done it with reasonable success. With noodles though, it’s more difficult to get a consistent and regular shape like a circle or a rectangle. I mentioned this to my girlfriend before I began this somewhat daunting task. She said that I shouldn’t worry…”It doesn’t have to be perfect.”
My goal, according to her instruction, was a very flat, roughly rectangular shape. I was able to accomplish this in a very reasonable four minutes. Now it was time to slice. The tool supplied for this was a rolling pizza cutter. The general guideline was to make vertical slices, but don’t worry about being perfect. Her exact answer to my question of “How straight?” was “Straight enough.”
The important part (went the explanation) was to “get the edges the right width” and then “make sure the interior slices are around the same width”. The next instruction was to slice the resulting long strips of dough in approximately equal bite-sized pieces. My immediate question was, “Your bites or mine?” While she’s not petite, I’m substantially larger than her. She’s a good cook, what can I say.
Anyway, I asked the question and then the answer struck me…do some of both. Her response was a little more pithy. “Just be approximate. It doesn’t have to be perfect.”
Since the edges of the rolled-out dough tended to be more wavy than straight, I elected to start at one edge and try to follow the contour, but not too closely. Yes, there were some strangely shaped pieces that looked sort of like a side-view of a just-fed python. But on the whole everything worked out without too much waste. If I had followed the exact contour of the edge to maximize usage of the available dough, then subsequent interior slices would have to be “evened out” as I got toward the center. But, if I had started in the center and tried to create as near perfect cuts as I could, I would have had way more odd shapes when I reached the edge, resulting in more odd shapes to discard.
I positioned the pizza cutter at the edge, and rather than execute a cut, I called my girlfriend over to fish for some constructive criticism.
Me: “This one would be too small, right?”
Her: “Yeah. If you made it a little wider, you could probably salvage more. You can’t smoosh the discarded pieces back together very well, and you don’t want to waste.”
Me: “So we’re using the entire area of the rolled-out noodles, but we’ll still wind up with some odd shapes where the edges were.”
I considered for a moment. “If we sliced them thinner, then we could have more consistently shaped noodles and have fewer oddly shaped ones.”
Her: “Yeah, but then they aren’t bite sized any more”
Me: “So we have to balance eatability with regularness?”
Her: “That’s not a word. But yes, something like that.”
Me: “So we’re optimizing eatability (yes it’s a word, dammit, let me finish) against waste!”
Her: “Um, if you spend all your time optimizing, we’ll never have any soup.”
Me: “Ah! So it’s actually an integration problem in three dimensions! Maximizing consistent size for eatability, minimizing waste for oddly shaped or too small bits, and constrained by time!”
Her: “Well, yeah. You didn’t see that before?”
She slowly shook her head with amused exasperation (as she so often does when I over-analyze things). “Alright, so you found an optimization problem. Good for you. However, you didn’t take into account that the original slice width was not only constrained, but irregular. Also, the slices weren’t straight. That adds further to the irregularity. So, your integration analogy starts to fall apart. Integration depends on the consistency and reproducibility of the slice width parameters. And, frankly, this sort of integration only works in two dimensions. So your rollout of the dough introduced a third dimension of variability!”
Yes, she is correct. Did I mention that my girlfriend used to work at JPL? She was a real-life rocket scientist.
However, it IS possible to do integrations in more than three dimensions. It makes your head spin, but it can be done.
In my defense, I did a really good job of rolling out that dough. At least I thought so.
In closing, I would assert that noodles and calculus really ARE the same. One is an illustration of the other, perfect in it’s imperfection. We use calculus to approximate an answer to a degree where the difference between the approximation and our desired outcome are indistinguishable. Further refinement becomes an academic exercise, with little practical value.
We cut handmade noodles to get just enough regularity for eatability and to identify a particular “feel”, but not enough regularity to make it feel artificially perfect. Eatability is definitely a variable that can’t be completely controlled for. I suppose that this explains at least in part why there are so many different varieties of noodle.
And so, we now have a true example of how math applies in real life. The soup delicious.