Excellent reply, Andy, and I am glad you are showing me your inner thoughts about finite and infinite, plus with it your overall brain's functioning. Nothing wrong with it.
Yet there is more, and I will start with the difference between the binary and decimal systems.
We often view 1 as representing the whole, or a unit. For instance, we can declare Unity as a state of 1.
But that is the decimal system doing the talking.
Now look at the binary system, and low and behold there is no Whole, no Unit, no Unity declared. That is, unless we establish it ourselves.
We can make 1101110010001 represent Unity in the binary system, as soon as we all agree on it.
With this information, we can look back at the decimal system, and then recognize that if we had eight fingers instead of ten, we would be using the octal system.
Clearly, we are using the decimal system because it provides us benefits over the binary system. Yet benefits is then another word for short cuts. With short cuts we can lose our grip on the grounded features of math.
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The overall truth has been declared as there not being any truth, and from this we learned something important:
Unless we declare the context, no content is ever well defined.
The example I often use is blue.
Blue means something different in the paint store than on the couch with the shrink.
We must declare the context, and that is often where we find concepts.
Note that blue is not a concept but a factual word for a specific color. Blue will be true anywhere in the entire universe, just like the chemical building blocks are true anywhere in the universe. We can speak with an alien by pointing at the periodic table, which the alien will recognize (the ordering may be ever so different for the alien, but all will be highly recognizable).
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Since you consider infinity an important concept, I have to address this from the content-and-context perspective.
Children can already grasp the concept of infinity, but it is complex to understand all the ins and outs.
Infinity turns out to not have any contents. It is a context about a condition we can recognize as such.
The example I often use is the apple. Cut it in half, and cut the pieces in half and continue to cut the pieces in half ad infinitum.
After thirty of such cuttings, we have apple sauce. After one hundred of such cuttings, we are loosing the ability to taste the apple flavor.
Long story short: We can start with a content and place it inside a context of infinity, yet it is the human brain that walks this to infinity while the contents disappeared rather quickly.
That is why I added the engineering joke, Andy, because they made it quite obvious that infinity is a concept inside people's heads and how it does not exist in reality. That is, with space the only exception.
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This is what I work with:
* Matter appeared 13.8 billion years ago.
* Energy does not get lost, so we can place immaterial energy in the starting position prior to the transformation of some of that energy into matter.
* Time and Space are phenomena, which means they are real but they do not have any attributes of their own.
* Spacetime is a framework, a tool. It is not about Space; it is not about Time. Newton and Einstein were working on explaining the behavior of matter. Not even Einstein said anything about Space or Time, but he used them to give his tool a name.
Let me start with this last part first, and a tape measure is simplest to show how Space and Time have nothing to do with the behavior of matter.
A tape measure accurately measures how tall you are. But no one would ever say that the tape measure was involved with how tall you ended up being, right? So, the tape measure is not part of how tall you grew.
Same for Spacetime, it is just a tool to express the behavior of matter.
I don't call it Spacetime, I call it the Fourth Motion, meaning I am explaining the Einsteinian behavior of matter with the fastest motion matter is involved in, which is the catapulting action of the materialization process. It started 13.8 billion years ago, and nothing stopped it.
Place an object outside its common Earthly position, and that Fourth Motion will be the greatest influencer of that matter’s behavior.
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Then, I have an easy example to show what a scientific phenomenon is: The Eye of the Storm.
The Eye of the storm is real, we clearly see it, and yet the reason for the Eye is based on wind force, and yet there is no wind force associated with the Eye. The reason the Eye exist is not based on attributes of the Eye itself. So, that is a phenomenon. Real, but no attributes.
Interestingly, the strongest wind gusts doing the most damage on planet Earth are found right next to the Eye, with the Wall of the Eye. We have a very important 0 in the middle therefore, and we have the most important 1 sitting right next to it, indicating maximum wind force, while further out that 1 diminishes all the way back to 0 with the edges of the storm.
Space in my view is:
* not ever moving
* without boundaries (no borders)
* not interfering with anything
Space simply is a phenomenon.
That is a lot to take in, Andy. I hope you like it.
Let me know what you think of this, and also tell me what you work with, if indeed you work with grounded aspects or not. You may be working with concepts only.
