Another Wavelength: Caleb Gannon

    Date Posted: 
    Monday, April 20, 2020

    This month in Another Wavelength, we chat with 5th year Ph.D. Student Caleb Gannon. Caleb is currently mentored by Rongguang Liang.

    Where are you from? 

    I grew up in Elgin, Illinois. About an hour away from Chicago, although I rarely went into the city.

    What brought you to study optics? 

    I had an exceptional professor in undergrad (Paul Leisher) who taught a few of my early optics courses. He assigned tons of homework which kinda beat an intuitive understanding of optics into me. By the time I graduated I somehow knew way more about optics than I did about my actual major which was engineering physics (think MEMS/semiconductor stuff).

    Who is your hero in science? 

    Right now I would have to say Kurt Gödel. He fundamentally changed the way we think about math and science with his incompleteness theorems. In these, he discovered that any formal system which is powerful enough to be interesting (non-trivial) will cause contradictions. Essentially, there are some things in mathematics and by extension all of science that might be true but fundamentally cannot be proven. Also the way he constructed the proof is incredible: he established a mapping from the natural numbers to mathematical symbols such that each sequence of numbers could represent a sequence of symbols. These numbers representing sequences of symbols are still numbers, and can be manipulated using formal theories of arithmetic. Using this, we can reduce questions about these statements to the properties of their numbers. Basically he found a way to allow arithmetic to describe itself and showed that such a construction is possible in any formal system, which will always lead to problems. For example in english I can say "this sentence is false" - a valid statement which is contradictory. We generally accept this limitation within language as trivial, but it's a hard pill to swallow when discussing mathematics.

    Describe your research in 20 words or fewer. 

    I use math to make designing things such as optics easier and faster.

    Describe your research in 200 words or fewer. 

    Designing anything is a strange problem: we can check the performance of what we have, but we have no idea how to get to what we actually want.  Exhaustively searching all possible solutions scales exponentially with the number of variables which is infeasible for most interesting cases. So there is no way to build a complete solution, we have to rely on approximate methods of solution - trading certainty in outcome for speed. One popular approach is to use the gradient of the problem space to guide us through local possibilities towards our goal. While this works (somewhat unreasonably) well, there is no way to know if what we find in the local search is the best solution. I am interested in seeing if there is a better way to explore the global solution space to a specified degree of certainty. Rather than an exhaustive search for 100% certainty taking exponential time, performing a targeted search that is willing to skip over regions it believes are not likely to produce good results. This behavior is demonstrated in Monte-Carlo methods, where questions about high dimensional problems can be answered extremely precisely using only a few evaluations. I am hopeful there is some way to formulate the design problem where it can be answered in a similar way.

    Name three neat facts about you. 

    1. I make AI generated art. (see the picture above!)
    2. I run a youtube channel where I play Magic The Gathering.
    3. I am working on becoming a halfway decent food scientist/chef.