The 7 Dimensions of Everything and Nothing ! Our 3, or more, Dimensional Universe ! Hilbert's Grand Hotel

Physics and numbers go together. Numbers help us to understand the deeper unseen processes that happen in the physical world that we live in and take the mystery out of every day events. We look at the world around us and try to make sense of what we see. We have an idea, feeling or intuition about something. We observe, experiment and take measurements. Unfortunately numbers can sometimes be just as mysterious as those every day events that we are trying to unravel. Sometimes numbers just don’t balance out, cannot be resolved or point to something else that we don’t understand. Numbers in Quantum Physics can be counted but can they be measured? Quantum Physics says both yes and no.

Because numbers, no matter how big or small, are subjective beasts, they can only go so far. When they stop we need to think outside of the box to fill in the blanks. Infinity and Zero have filled in some of the blanks that have allowed us to get where we are now with technology. Everything (Infinity or ≠0) and Nothing (or 0) are used as values in most things we take for granted these days. It doesn’t matter how hard we try we can never physically get to Infinity or Zero, but, they are both essential in describing a set of something that can’t be measured until someone devises a way to measure it, for example our Universe or even Pi.

The idea of Everything only exists because something exists that can’t be measured or counted. If something can be measured or counted then it cannot be Everything. The idea of nothing exists because there is no other way to define its existence or lack of existence. I remenber reading about the early European explorers that first visited Australia. They came back with stories of strange animals including the Black Swan. They were ridiculed and treated as hoaxers. Nobody believed them.

If I asked you how many green and black striped oranges or apples were in a barrel of oranges, how many would you say? If you said “0” or “None” does that mean that green and black striped oranges or apples don’t exist? A Set is a container (Barrel) that contains something or groups of something (Oranges or Apples) or even nothing (Empty). Just because an Empty Set does not contain what we are looking for, it does not mean that it is empty. It only means that it has’t been filled with what we are looking for. Maybe there is other stuff in there that we are not looking for or can’t see.

Hilbert's Grand Hotel (a thought experiment, Paradigm or Paradox) describes the idea of infinite sets of infinite numbers within each other, within Infinity. There is a hotel with an infinite number of rooms with a person in each room. The hotel also has room for an infinite number of people in an infinite number of buses.

An Infinite set of numbers cannot be defined. We can define different subsets of types of numbers (or groups of similar values and/or properties. No two or more numbers will have exactly the same value AND property) of numbers just as we can define different subsets of people in the hotel or the buses into groups of similar ages, gender, hight etc. depending on what we are measuring or counting. But can we ever measure or count the total number of members in each subset? Quantum Physics would probally say both yes and no. It depends on what we are measuring or counting. For example 1, 2/2, 3/3 etc. If we measure 1, 2/2 and 3/3 etc. we end up with the same numbers, but if we count 1, 2/2 and 3/3 etc. we have different numbers. 

The idea of Everything only exists because something exists that can’t be measured or counted. If something can be measured or counted then it cannot be Everything. The idea of nothing exists because there is no other way to define its existence or lack of existence (The 7 Dimensions of Everything and Nothing).

Although the experiment does not explicitly say how the people originally got into the hotel or the buses in the first place, I feel it is safe to infer that they were waiting outside the hotel/buses and were then randomly given or issued a room key/seat ticket as they entered the hotel/buses (bijection, bijective function, or one-to-one correspondence).

 First thing is to establish what we are trying to achieve; to fit all the people in each bus with the people already in the hotel into their own room.

These people could also be divided into any other number of Subsets.What Sets are we working with?

If the manager took the infinite people out of the hotel at the same time as the infinite number of people got out of each bus as it arrived, he would have only one set of infinite people? He could then fit the infinite number of people outside the hotel comfortably into the infinite hotel. Each person would have a key to their own room using the above bijective function. 

If the hotel had an infinite number of levels the manager could also fit all the infinite people that came out of each level and bus and fit them all comfortably into each corresponding level of the hotel.

This would mean that there are no empty rooms, and each person from the hotel is only disturbed once.