Is it POSSIBLE to understand a singularity?

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The singularity is, hands down, the single biggest mystery in the known universe. In a singularity, space, time, and all known laws of physics fall apart. Scientists believe that understanding the singularity will require new physics, but where are we going to get these new physics? Theoretical physics is based on previously-proven facts of regular physics, and regular physics is based on observation. The first theoretical physicists derived their theories from known concepts of Newtonian physics and quantum mechanics, so observational physics provides the foundation for theoretical physics. So since the singularity of a black hole does not follow the known laws of physics, we have to go back to square one, but we have nothing to work with. Understanding science relies fundamentally on having something previously known -- such as an observation or valid theory -- that can start a "chain reaction," if I may, to lead to another conclusion, but with the singularity, the laws of known physics fall apart, so theoretical physics becomes useless, and the singularity is covered from view by the event horizon, so observation is impossible. Therefore, the only ways we can engage in scientific research -- observation and theory -- are thrown out the window. So where are we going to get these new physics? The known laws of physics were understood by our ancestors only because they had observations to get the wheels in motion. What are WE going to do with the singularity? We have nothing to work with. So what I'm asking is this: Is the singularity so strange that we can never hope to understand it, and science is wasting its time trying to do so? Your thoughts?