There is this wonderful youtube on the Spinning Dancer. I am wondering if you have seen it, Rich.
https://www.youtube.com/watch?v=2RSsoTJA6cA
A large number of people get stuck on seeing the ballerina dance in one direction only, but perhaps you can see it spin in opposite direction, too?
Here is the youtube that shows both visual directions through adding details that guide the eyes.
https://www.youtube.com/watch?v=bR_lD1g_5JY
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The best information Intuitive Mathematics provides is the already mentioned confirmation about the human brain using many different tools, and how each tool is always limited to doing what that specific tool can do.
As such, the black&white desire we all have to keep information locked in a specific spot and then have it be true forever and ever, that desire needs to be kept under control. Not an easy task. It is so easy to say, male/female and then consider all said and done : - )
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What you may consider from a structural thought perspective, Rich, is looking how each system (each tool) can be built on different structural grounds. Keep in mind that there will be gray areas.
As example, I view religion mainly as a top-down approach. With a single God or with a group of gods, we start with the highest and mightiest position, and then everything underneath falls (supposedly) into place.
In science, the approach is more bottom-up, starting out with collecting data from the real world, and then slowly moving up toward the larger levels.
A gray area in science is that one can indeed jump to a higher level, either through theorizing or simply starting with a hypothesis at the higher position. Yet the higher position must ultimately be based on something that is correct at ground level. So, a hypothesis can hang in the air, but only for the duration of the investigation whether that hypothesis makes any scientific sense, or not. If not, then there is little value given to the hypothesis.
A third structural group I find important are the philosophers. I like them a lot, and they annoy me, at times enormously.
In philosophy, one starts out with concepts, accepted to be understood by everyone. Yet once the concepts are accepted, folks tend to not delve in to the deeper, real-detailed level. This can be fantastic, and this can be annoying (for me).
The example I often use is Democracy, and how everyone places it in a specific spot and then discusses what is so great or bad about Democracy. It irritates me tremendously how few people compare different forms of democracy. For example, UK's first-past-the-post (about 42% of the voters get the one they voted for) is nothing like Sweden's proportional system (about 99% of the voters get the one they voted for).
We are really talking about two completely different systems here. In one system, an elite group controls the outcome (50% of 42% is at minimum 21% of the voters supporting the decisions made). In the other system the majority controls the outcome (50% of 99% is at minimum about 50% of the voters supporting the decisions made).
The point once more is that philosophers can hang with the concepts and don't move to the level with the exacting details.
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Allow me to mention once more that matter is circling, but matter is doing something else as well: moving in a straight line.
The Milky Way, for instance, is circling around itself, but it is also speeding at its highest velocity in a straight line through space.
Using just Einstein's Spacetime, physicists are amazed how the galaxy should contain more gravity than there is to keep the outer arms as part of the galaxy.
But they are missing out on the straight action. Einstein's Spacetime is based just on the gravitational motions and not on all motions of matter.
When 200 ice skaters are skating at the same speed, in the same direction, at the same time across a frozen canal, then it appears as if they are a group.
Indeed, we can see group behavior.
Yet each skater is skating under his or her own power. The group does not power the skaters, except through camaraderie.
Same for the masses in the Milky Way. Ever since the Big Bang sent off this energy/matter in this one particular direction, all masses have been moving each on their own accord in that direction, at the same speed and time as the other masses.
So, physicists are focusing too much on the circular motions, and do not take the straight line motion into account well enough.
Thank you for sparring with me. I appreciate it much, Fred-Rick
