Our eyes only see the big dimensions, but beyond those there are others that escape detection because they are so small.
In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.
I've seen children's eyes light up when I tell them about black holes and the Big Bang.
The pinpoints of starlight we see with the naked eye are photons that have been streaming toward us for a few years or a few thousand.
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