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Student B.S. Engineering, Cooper Union for the Advancement of Science and Art


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How can computer models help us build intuition?

The use of visual diagrams to explain and understand difficult concepts is as old as history itself, but in the twentieth century, for the first time, engineers and scientists were able to enlist the help of computational tools to represent systems with greater clarity and detail. While computers, with the right peripherals, are able to present data to all the senses, in two or three dimensions and through time, perhaps their greatest pedagogical virtue is their interactivity. People learn by doing: young children internalize Newton's Laws long before their first formal physics class by manipulating the world around them. Computers offer the promise of similar interactivity for systems which are less readily accessible, or even entirely esoteric. In my Bioelectricity class, for example, we have been using computer simulations of the complicated Hodgkin-and-Huxley membrane equations to gain insight into neural reactions to various experimental stimuli. How can computer models be used to learn, understand and ultimately build intuition about systems in nature and science?


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    Feb 15 2012: A challenge inherent in using computer models to build intuition is that often the computer models themselves can be built on faulty intuition. For example, a simulation like SimCity is based on a set of assumptions about what motivates people and makes them happy. It's difficult to build a successful city in that game without embracing and internalizing those underlying assumptions. This can be dangerous because of the power of these interactive computer models as learning tools. While computer models can be a powerful way to build intuition, there are generally no safeguards to ensure that the intuition they help build is actually valid.
    • Feb 15 2012: That is an excellent point. Alan Wolf, a professor of physics at my college, published an article about electromagnetic field line diagrams and the faulty assumptions on which they are based. These often computer-generated graphics are used to teach countless numbers of students electromagnetics every year.
      You can find the paper here: http://www.physics.emory.edu/~weeks/lab/papers/wolf-ajp96.pdf
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        Feb 16 2012: cool! go alan, go alan...its ya birthday
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      Feb 16 2012: I agree James. Often someone designing a simulation has to make simplifying assumptions, and it can lead to a misalignment between what actually happens, and what is shown to happen in the simulation. However, if you can compare the simulation against raw data and there is a strong correlation, then the construction of a simulation may give you some insight into the mathematical properties of the phenomena you are simulating, even if you can't articulate those phenomena explicitly using a mathematical model.

      However, you do really need to ensure that you are thoughtful in your use, and you don't assume that what you have provided is an accurate measure of reality; you need to check.
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        Feb 21 2012: David,

        I agree with your point and would like to expand on it. As you state, "you don't assume that what you have provided is an accurate measure of reality." I believe one would need a pretty solid basis of certain material before using simulations. The solid basis would allow one to have an intuitive understanding by interpreting the material "with a grain of salt".

        Sometimes these models aren't the best way to have an intuitive understanding. For example, when talking about having an intuitive understanding with science, lab work and hands on work lets you see exactly how much of an assumption you must make. Lab work lets you see how a real life application can lead to different results than expected. I believe the struggle of hands on work can lead to a better understanding than just a computer model.
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      Feb 17 2012: On another note, intuition on any level may be bad. More times than not, one would have to dive deeper and understand the roots of what one is trying to make a conclusion from intuition, and by then, the conclusion is not based on intuition anymore, it's based on experience and knowledge.

      For example, I've had someone ask me where they can get an ethernet "y-splitter". They wanted to share their network connection by using a y-adapter for ethernet. Intuition from other devices (rca, bnc, stereo, etc) tells us we can do this. One may argue, "of course!, networking is complex and it requires two way communication, so of course you can't split the cable that easily". But, before ethernet, there was thicknet, which was essentially one giant coaxial cable shared by multiple computers, yet they can do two-way comm. (so with thicknet, you can use a y-splitter). Rather, one needs to know how ethernet protocol works. One would have to understand how it works before they can conclude that these mystical ethernet y-splitters do not exist. However, even after having that knowledge, one cannot use intuition to construct their own network hub. Ok, say they learn how network protocols work, they still cannot construct their own network hub, they need to learn about signal propagation to know that certain long wires need to be in twisted pairs. One can find similar kinds of issues with any topic of study.

      We may say intuition is useful, but to me, it's not any better than a coin toss (that is unless you have more knowledge, but by then it's not intuition)
    • Feb 17 2012: What is needed is some level of wikilike interaction with the model, then, it sounds like, a 'backstage' or a way to tag stuff where people can communicate their doubts or maybe in a more formal circumstance discrepancies between what is observed and what's modeled, so that this data can drive the creation of new models.
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      Feb 21 2012: James,
      While what you and Simon are saying about simulations incorrectly portraying the information may be somewhat correct, the overall point of them is to simulate, not give a 100% accurate representation. It's this simplification that allows us to develop intuition for such things, since our minds can have a hard time building such complicated models on their own. Using the example of Professor Wolf's paper on electric field lines, we all admit that the current diagrams are flawed. But it's these flawed pictures that help us gain intuition of how electric fields act in general, and we can then extend this understanding to a full three dimensional picture of electric forces and fields. I think as long as we remember not to take a simulation to be the reality, they can be an invaluable tool.

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