Multidimensional Thinking in a Three-Dimensional World
The gritty details that underlie most engineering projects can often go unnoticed by the average person. Unit conversions, which are drilled into the heads of high school chemistry students and then promptly forgotten, can have large impacts in practical settings. In 1999, NASA’s Mars Climate Orbiter unexpectedly crashed into the Martian surface after failing to execute the tasks that would place it safely in Mars’ orbit. The ultimate cause of this failure was found to be that between the two teams working on the project, one used English units while the other used Metric units. These are not compatible with each other and while NASA’s routine programming checks allowed the craft to successfully reach Mars, it failed to detect the difference in units during the final leg of its journey. As a result, the spacecraft was lost. Now, not every failure to convert units correctly results in expensive machinery literally crashing and burning. However, it is paying attention to details like these that helps produce successful engineering projects.
The average person might not come across unit conversions often in their daily life. While they can be seen in cooking or purchasing certain products from overseas, people can manage them by simply using a conversion table or making reasonable guesses. Everyday decisions rarely require precision to the thousandths decimal place. However, a knowledge of these conversions and the different unit systems could make it easier for people to approach the world with a more scientific mindset. A recurring concept in one of my engineering classes is “Here are the units you will be doing your work in, which are not necessarily the same units your future client may understand.” If people had a better overall understanding of the multiple systems of units that govern our world, it would improve the ability of engineers and clients to communicate their needs and requirements for a project. Similar to the way speaking more than one language can enhance a speaker’s problem-solving and communication skills, being able to speak in different basic scientific languages can help change the relationship between science and society.
A major example of this is the ability of people to understand vector coordinate systems. At first, it may seem harder to connect this to the everyday experience. A vector is generally shown as an arrow with direction and magnitude. In its most basic form, it exists as an extension of the standard two-dimensional, xy coordinate system used to plot a graph. In a more practical sense, it is part of a larger three-dimensional coordinate system, and it can help represent the position, velocity, acceleration, and more of any particle in space. These vectors can be added, subtracted, multiplied, divided, and rescaled to represent any number of additional quantities that help better define the movement of an object in any direction. There are also multiple types of vector coordinate systems that are used based on the specific problem at hand. The ideal system depends on the type of motion, such as whether the object in question is rotating or moving as a projectile. Expanding the definition may not make their use to people clearer. However, just like unit systems, a general knowledge of vector coordinate systems could help people better articulate their desires for engineering projects. While they appear to be less important to everyday life, they have a wide range of applications and are necessary for understanding the physical laws that govern the world.
The real issue with vectors is trying to understand a three-dimensional system shown on two-dimensional displays. The human mind can struggle to visualize what an arrow in three directions looks like. How well can an average person break that three-dimensional system into three two-dimensional planes and understand the same vector’s orientation and meaning in all of them? Results may vary. In a world of complex problems, it is important to understand the system in which those problems are set. Vector systems are a mathematical application of spatial-reasoning skills. Einstein, Hawking, and other great scientific minds attribute their discoveries in part to powerful visual-reasoning skills that allowed them to get inside the world of their problems. Human limitations are related to those of the characters in Flatland, a book and film where a two-dimensional figure (a square) investigates one-dimensional (line) and zero-dimensional (point) figures, and is shocked when a three-dimensional figure appears and helps him understand what it would be like to discover his coordinate system had an entire axis he had never explored. The reader or viewer is also able to explore the theoretical four-dimensional shape imagined by mathematicians. However, humans struggle to fully comprehend the idea of the fourth dimension.
While complicated math and physics are needed to produce many great engineering feats, a basic understanding of the core concepts behind them can elevate an average person and help them better understand the world as a whole. These concepts that are vaguely introduced in high school science courses are based in the simple arithmetic and visual analysis that we are encouraged to develop as children. Pushing these important details can improve our problem-solving abilities and communication skills on technical subjects. Enhanced analysis skills can further society’s technical advancement and make complex science concepts more understandable. Our ability to think like engineers can help us better navigate our three dimensions and any dimensions that lie out of sight.
"The Advantages of Being Bilingual." American Speech-Language-Hearing Association, ASHA, www.asha.org/public/speech/development/the-advantages-of-being-bilingual/. Accessed 14 Feb. 2019.
Flatland: The Movie. Directed by Dano Johnson and Jeffrey Travis, 2007.
Frank, David, and Duane Q. Nykamp. "An introduction to vectors." Math Insight, mathinsight.org/vector_introduction. Accessed 14 Feb. 2019.
"The Importance of Spatial Reasoning for Children." The Children's School, 17 Mar. 2017, www.childrensschool.org/posts/importance-spatial-reasoning-children/. Accessed 14 Feb. 2019.
Isbell, Douglas, et al. "Mars Climate Orbiter Team Finds Likely Cause of Loss." Mars Polar Lander, NASA, 30 Sept. 1999, mars.nasa.gov/msp98/news/mco990930.html. Accessed 14 Feb. 2019