This is helpful, Rex, because you write your argumentation down in specifics, and therefore I can show you where you glob things together that are not of one and the same system.
"The entire analogy with decimal vs. binary is completely unhelpful. The representation of integers is isomorphic between the two. In particular, 1 is the unit in both because (1, +) generates the entire positive branch of the integers, regardless of whether 1 is written in a decimal representation or binary representation."
You have to pay close attention to see the following. When you are using 1 to represent the entire positive branch of the integers then you are using the decimal 1 and you are sticking it on top of both the decimal system and the binary system.
Of course the brain has no problem doing that, but you are forgetting that in one case you switched systems. You correctly use 1 to point at the entire group of numbers in the binary system. But try to do that while using the binary system and you cannot do that; that option is not available unless you make it available.
For instance, if you say that from now on 1000110110 represents 'the entire positive branch of the integers' then we can shake hands and say okay let's call it out that way for these binary system numbers using the binary system numbers.
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There is a third numerical system, even though it is not a real system because there is just one number in that 'system'.
The system that contains just 1 as the only member is a small category; there aren't too many examples to use it.
Words like Universe, Everything, Life, All, Mankind, Whole, God, and Nature occupy this system.
They are generic words, they are almost like labels, though we understand their 'specific' meaning.
As example, when reading an article with as title "Mankind and the 20th Century" then we don't have a problem what the article is about. Yet the title contains two numerical systems. With Mankind, we have the generic term indicating anything about people. With the 20th Century, we abandon the generic system and dive into the system with specific articulations.
Ordinarily, this difference is completely unimportant, let's agree on that right away.
Yet when we stand at the overall level, then that tiny distinction is important because we can see the two different numerical systems at work. We can stay at the overall level or we can dive into the specifics.
While Universe is a word everyone understands well, the structural question is whether we can apply a single structure to it and be done with it. Again, Gödel told us that we cannot, but it is also easy to see.
When starting out with Universe, we can't formulate a single platform to express all our knowledge. Not only are unknowns included in the term Universe, but we have to pick which system we are using as well. Are we using the generic system with 1 word, Universe, and deliver a single truth about it (which could, for example, be picking between 'unified' or 'not-unified')? Or are we using the decimal system and build ourselves an astronomically large list of all the things we know plus all that we suspect what is out there but for which we don't have the evidence (yet)?
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If you are not seeing it still, Rex, then I am hoping you will articulate yourself the same way you did now. Naturally, it will be easier to show the underlying structural reality when we discuss numbers than when we use letters or names. Already with having numerical systems and many systems of language, we should know that there is not one single universal system.
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The point I am making is that a unified field of forces is not available at a single level, but must have at least two layers to their overall reality.
If we take the four forces and recognize that the GUT is indeed established, but gravity is not well-linked in with this group yet, then moving away from using one layer and embracing two layers instead can really make the difference.
First an analogy, then the forces:
* Mothers
* Fathers
* Children
* Families
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* Strong-nuclear force
* Weak-nuclear force
* Electro-magnetic force
* Gravitational force
—
The first group is to easily show you their structure, the relationships among the four of the first group, but also of the second group. The analogy here helps to show the structure.
We can see that while we have four distinct parts, we actually have just three distinct parts in essence, but that the fourth part results automatically from the first three parts.
As such, the human brain has no problem solving this 'problem' but it can then also not be done on a single level. Rather, we see a tetrahedron (or a pyramid if we use electric force and magnetic force as oppositional to one another). There are (at minimum) two levels.
In the GUT, we find all are related, so what we are looking for was indeed established already. Yet by approaching gravity as a separate force all by itself, we will not be able to create a single platform on which all fit. Not possible because the exacting truth is not applied.
Gravity is the synergistic outcome of the other forces. It is therefore a force and not a force at the same time, and there is no problem calling gravity out as a force or as not a force.
Thank you, Rex, for this reply you provided. That was helpful for me. I hope this is helpful for you.
