November 18, 2003
Force-Field Embrace... Let's take five with Moira Gunn. This is "Five Minutes".
Technology is a product of science and engineering. Science reveals the truth about the natural world, and engineering uses that truth to build technology. Of course, just as often, engineering figures out how to build something, and science paces around scratching its head, pondering just how in the heck that could possibly be. And eventually, new scientific truths actually emerge.
Look at this interchange long enough and you realize that there is a force-field embrace between science and engineering which fuels all the technology humanity has ever built.
What's missing in this perspective is the role of mathematics. And why? Well, science and engineering have a tendency to view it as a useful tool, and not much more. Mathematics can reflect the truth, but also mislead. You see, something can be mathematically consistent, yet not exist in the natural world, the place where science, engineering and technology must necessarily live.
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The example that I use the most concerns a mathematical model which was developed to lay out the pipelines in a new oil refinery. If you've ever driven past one, or seen a picture, you can appreciate the hundreds, if not thousands, of feet of pipe running everywhere. Your eye follows a row of pipes, only to see several peel off at an angle. Huge ones run low along the ground, while narrow ones soar high above tanks and among outbuildings. You can easily imagine what a challenge it must be to get it right.
The math model for such a problem has to recognize the viscosity of the fluid at every moment: Crude oil is as different from gasoline, as oil is from vinegar. And then there is the quantity being moved, the temperature and the distance to travel. And that's just for starters. There's every reason to optimize, including the simple fact that pipes cost money.
To meet these challenges, math models are developed and programmed into computers, where various layouts are generated and tested. And that's where this particular team's problems came home to roost.
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The team was thrilled that everything was flowing everywhere at top speed, until an old hand took a look and realized that something was very wrong. When you move anything through a system, there's always a price to pay, and he started looking for flaws.
Eventually, he realized a novice programmer had forgotten to include the "non-mathematical" constraints to the program, specifically, the realities of the physical world. His optimization algorithms let the inside diameter of a pipe increase to a size larger than the outside diameter. Oil within this model flowed friction-free and unaffected by gravity. Yet the mathematics was consistent. Too bad you couldn't build such a pipe in the real world.
Before you label mathematics unreliable or useless, look again. Take the physical world into consideration, and mathematics will tell you if your plan will work.
Without mathematics we would not have the Acropolis or the Pyramids. We'd be without Leonardo da Vinci's hand-drawing of the perfect man in the perfect circle. We could not theorize on what lies beyond our solar system, or break down the human genome.
And for all of that, mathematics is solely a product of the human mind. You cannot touch it, or find it lying under a rock or in a cave. It has no beginning in religious tradition or basis in faith. It only survives by each generation of humans teaching the next. It is uncompromised by differences in human language, or culture, or individual experience.
In its universality and consistency, mathematics is perhaps the purest of all tributes to the extraordinary capability of the human mind.
I'm Moira Gunn. This is Five Minutes.
