Hey, you know L. E. J. Brouwer? That's great, Dr. Rich. I stumbled on his work years ago, and really like where he (and others in his day) were going.
The early decades of the 1900s were a fascinating time of discovery, and it is fantastic to see how they did capture everything correctly, and then veered off into the woods somehow.
It is with the later discoveries that we, humans, sharpened our vision, removing the incorrect aspects of the earlier 1900s.
Yet it is like the Aboriginals. Scientists are still waking up from the Dreamworld, and there is a sincere avoiding going on by a large number of them, not wanting to wake up.
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Rubin's Vase is one of the vehicles to understand the big picture. One has to delve into the details, though, and that is what many avoid (and therefore miss the clarity of the big picture).
Let's see if I can show it in easy words.
The image of the Vase inside the entire image is, expressed in numbers:
0 - 1 - 0
The two zeros represent the unimportant space around the Vase. The Vase is the 1.
Here is the image of the Two Faces:
1 - 0 - 1
The two 1s represent the Faces. The empty center is the 0.
These two images cannot be melded into one. They contradict one another in an important aspect.
Either the universe is based on the Vase, meaning unification is possible, or the universe is based on the Two Faces, meaning unification is absent.
The beauty lies foremost with zero.
The two zeros of the Vase are declared background to the Vase and are by themselves unimportant.
The single zero of the Two Faces is declared background, yet is vital to the outcome. Had that space not been there, then there could not have been Two Faces. The zero declares the independence of each Face.
Most folks do not realize that zero is not a single number. They think that 0 is singular like 1 can be singular.
But not even 1 is truly singular, unless we declare it as such.
No number is singular. I'll show that for 1 in a second.
Look wide and far and there is no system available in which unification is established, except for the labels, for the concepts themselves, that point to the whole: Universe, All, God, Nature, Life, Mankind, Everything.
These all-inclusive words do not contain any details, so they function like Rubin's Vase; there are no decent opposites to these all-inclusive one-words. There are zero backgrounds, like Death next to Life, Nothing next to Everything, the Devil next to God. Yet these are also not words that point to details. They exist at the overall level, and that is where they get their meaning.
Please recognize how the Vase belongs to the Black&White department of our brain.
The Two Faces, that is a different story, with details that are important. These are colored options, not Black&White.
Allow me to work that out with an example.
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In ancient Greece, a cultural mistake was made of trying to turn everything into male or female objects (other cultures did so too), like making the Moon male (or female).
System-wise, the male/female system appears to deliver a completeness. The two expressions cover all options, right?
But... a rock is neither male or female.
This is a very simple way of showing (once more) how systems cannot express all.
For the rock, the male/female system has to express itself with a zero for both options. The system cannot complete the task because the system is limited in expressing itself.
Mathematics is also a limited system, but we have a hard time recognizing its limitations because it does such a fantastic job helping us see a lot of nearly everything.
But an Incompleteness it is nevertheless. Mathematics expresses only that what can be expressed mathematically, and nothing else.
A quick way to show this is with the building blocks of the decimal system:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
This entire set of building blocks can be declared with 1. One can say that we have 1 entire set.
Yet I did change systems on you here, you probably noticed.
The first 1, from the set itself = unit.
The second 1, about the set itself = whole.
Twice I used 1, but I used two different systems nevertheless, and many people are not paying attention to staying inside the lines of systems.
It appeared I used a Black&White number, but then specific colors showed up.
So, the real task is to show people that they are always thinking inside a system, but how everyone can be sloppy, not staying inside the system they started out with, jumping into another system, unaware.
Ordinarily, not-staying inside a system is totally unimportant. The primary task is to communicate, and as long as the other got the message, via correct or incorrect pathways, we are all good. The message was delivered. Hooray.
Yet when we want to have a look at the big picture, then our brains must be aligned properly, otherwise we end up fooling ourselves, embracing Black&White truths. Then one can end up stating "We don't know" as the final answer.
So, that is the assignment, Dr. Rich. You must align all your words in their appropriate systems, and not step a single foot outside a system without understanding that you stepped outside the lines you started out from.
One cannot say that 1 man and 1 woman ended up as A. You know perfectly well what I mean, and the point in this is not about understanding the message but the structure itself. 1 + 1 ≠ A. Bad structure.
While embracing Gödel, one can know that there is no single system that can deliver a completed outcome, other than that what fits completely inside that system. No system exists at the overall system, except for Black&White positions that are not natural positions.
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The brain is a tool, and the entire universe is NOT found inside the brain. Yet the brain can capture the entire universe inside the brain. The brain is a tool, so it can do that. That means we have a natural note block inside our head and we can write down anything we want on that note block. But the words and visuals on the note block are never the real deal. Recognize the brain as a tool, and you can see yourself looking at the big picture, Dr. Rich.
Thank you for your further replies. I really appreciate them.
