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I have a feeling that it might be interesting to pursue a direction like aerospace engineering if I happen to get accepted. (Whether I have the ability for it is another question to consider.)
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It seems like Caltech is more focused on STEM subjects than liberal arts. However, it’s worth noting that while the stereotype of a Caltech student is a math-geek and engineer who dislikes humanities, there are actually many students who have a strong interest in fields outside of science. About half of the undergraduate students at Caltech are not solely focused on science and would be interested in discussing topics like literature or psychology.
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It feels like Caltech has a similar position to universities in Japan like Tsukuba or Tokyo Institute of Technology.
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As for majors, it seems like starting with the Shimojo Lab would be a good idea. The Computational and Neural Systems program seems suitable. CS also seems enjoyable, although more focused on theory. EE, Eng and App Sci, and MechE are also options to consider.