Sure, Sycamore, that would be my pleasure.
In 1981, I recognized what the Structure of Everything is, and from that point on I investigated what philosophers and physicists and scientists have said about it.
In my quest to see who knows what, Gödel entered the picture. Later on I learned he was best buddies with Einstein, and there is a lot more to say about him. Here are some personal aspects to read on Wiki:
https://en.wikipedia.org/wiki/Kurt_G%C3%B6del
What I consider most important of his work are his Incompleteness Theorems. He was curious and set out to investigate mathematically if one can start with a given setup and then end up at the overall level with that given setup not only intact but also informing and helping explain that overall level.
It turned out that he ended up discovering that no matter what he used to start out with (axioms), there was no way that it could be the truth for the big picture level by itself.
While at the big level, we do find Everything there is, the 'complete kit and caboodle', but the mathematical information declares it an Incompleteness nevertheless. The whole isn't whole.
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Allow me my simple examples to inform you on this, noting that many physicists love to reject the importance of Gödel's work (and my simple examples as well).
When we discover a truth about boys (for instance, having the ability to grow a mustache), we cannot take this truth and apply it to all people.
This simple truth leads then to Gödel's First Incompleteness Theorem. We can swap out the boys' feature for a girl's feature true for girls only and end up with the same kind of incompleteness about all people.
The Second Incompleteness Theorem is found while starting out with both truths at the same time, to see if we can then get a complete picture about the larger reality, letting both truth be what they are.
Again, an Incompleteness is the result because we will have to end up adding fig leaves to Adam and Eve.
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A little more about Gödel that fascinates me is that at one point (and I should find out when he said this, before or after finding his Incompleteness Theorems), he proffered the question whether the universe as a whole could spin.
That is the complete opposite of what a person, understanding that Incompleteness through and through, would say. So, it appears that Gödel stumbled upon this information, was curious about it in a 'simple' manner, and did not realize he figured out something that declares a fundamental aspect about our universe (meaning, that it is not a unified reality, but a broken up realities like pieces of a vase).
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The Structure of Everything is a pyramid.
At the four corners of the pyramid, we find the specific truths, for instance, young, old, male, and female. Again, all quite simple.
Combined, they show us the big picture, but there will never be a single person who is young, old, male and female all at the same time.
So, looking for Unity (or Completeness), the top of the pyramid is shown to not be based on solid grounds, but rather is slowly built up piece by piece from the bottom until we reach the top.
We do find Unity in top, but we have to use words that do not give away all details. For instance, we are all human beings. We found ourselves therefore a unit that applies to all of us. Yet we had to 'lift off' from the detailed ground and move to a higher spot where we are further removed from those details.
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I hope this helps a bit, Sycamore. Thanks for being interested in this kind of perspectives. Gödel definitively was very much into all this structural stuff.
