What is reality?

If a tree falls in the woods and nobody is there to hear it does it make a sound? The answer depends on how you define your terms but I usually argue that the falling tree makes vibrations in the air but they are only sound if they are experienced as such. We live in subjective reality. We perceive everything through our very limited senses then experience them relative to our own experiences, temperament, and prejudices, then over time our memories of it fade and we invent things to fill in the gaps in our knowledge. Our own reality is how we experience it. There is an objective reality independent of our perception of it but it is beyond us. The philosopher Ayn Rand felt we can experience objective reality through rigorous application of observation and reason. I hold that we can figure out a lot of things through observation and analysis but we are so limited that what we do know is only a tiny fraction of all there is to know. The mathematician Godel turned the field of mathematics on its head by proving that not all true statements can be proven and not all false statements can be disproven. To me this goes against Rand’s Objectivism showing that objective reality is beyond us no mater how rigorously we observe and analyze.