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

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).

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

Set A = hotel,

Subset of A =
{} = Rooms not available as Guest rooms, manager’s bedroom etc...

Subset of A = A1 = Guest rooms.

Subset of A = A2 = Person in each room in the hotel,

Subset of A = A1 = Guest rooms.

Subset of A = A2 = Person in each room in the hotel,

Set B = Bus

Subset of B =
{} = Seats not available for passengers, driver’s seat etc...

Subset of B = B1 = Passenger Seats on the bus.

Subset of B = B2 = Person on each Seat in the bus.

Subset of B = B1 = Passenger Seats on the bus.

Subset of B = B2 = Person on each Seat in the bus.

Set C = Number
of people

Subset of C =
{} = Staff of the hotel, drivers of the infinite busses etc...

Subset of C = C1 = People in the hotel.

Subset of C = C1 = People in the bus.

Subset of C = C1 = People in the hotel.

Subset of C = C1 = People in the bus.

Room
{} = Empty Set. Manager’s room etc...

Room 1 = 1st Guest,

Room 2 = 2nd Guest,

Room 3 = 3rd Guest,

Room 4 = 4th Guest...

Room 1 = 1st Guest,

Room 2 = 2nd Guest,

Room 3 = 3rd Guest,

Room 4 = 4th Guest...

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.

Hotel:

Ground
Level or Level 0 or {} = Empty Set. Rooms not available for guests.

1st bus = Level 1, Room 1.1, 1.2, 1.3...

2nd bus = Level 2, Room 2.1, 2.2, 2.3...

1st bus = Level 1, Room 1.1, 1.2, 1.3...

2nd bus = Level 2, Room 2.1, 2.2, 2.3...

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

There are at least 5 other ways to fit the
people into the hotel,
however it seems to me that there will be at least 1 person always
looking for a room when we use any of the these methods because every
room is already occupied. There is also the possibility of ending up
with rooms that are empty.

This thought experiment is actually describing four different types of infinite sets...

This thought experiment is actually describing four different types of infinite sets...

1.

The size of the hotel/buses are unmeasurable because their dimensions/ volume cannot be measured. If the hotel/buses could be measured they would be finite. There is no such thing as half a room in the hotel or half a seat on each bus. There can only be a room or a seat, no matter how infinitely big or infinitely small. The hotel manager could easily fit all the people from one bus into one room in the hotel. Our Universe is the probably the best example of an infinite space because it can’t be measured and it is expanding faster than expected. Quantum particles are also an examples of an unmeasurable set. We can only approximate what we see. The value of Pi could be considered an unmeasurable set because it can’t be measured.

2.

Which is the bigger set, the infinite number of people in the buses or the infinite number of people in the Hotel?

Any set of numbers, values or objects can be counted, even if they are not there. We have a bucket of oranges. We start from 0 for nothing and then 1 and then 2 etc. and we end up with a finite number. But, there are things that we can count and never get to the end. We can count numbers by adding 1 to the previous number and never get to the end. Could we ever count the infinite number of people in the hotel or the infinite number of buses? Will we ever get to the end? Mathematics has never been able to count the total decimal places of Pi and probably never will.

3.

How many numbers, values or objects can you count between 1 and 2? Would you ever get to the end? How many numbers, values or objects can you count between 1 and 200? Would you ever get to the end? Does this mean that the set of numbers, values or objects between 1 and 200 is greater than the set of numbers, values or objects between 1 and 2, or, does this mean that both sets are subsets of the of the set of numbers, values or objects? Or, are the numbers, values or objects just a set of infinite subsets of itself.

The people in the hotel and the people in the busses can be treated as two subsets of the set of all the people and two empty sets. The hotel is a set that contains 1 subset of infinite guest rooms and 1 Empty subset of rooms not available for guests. The infinite number of buses each contain 1 subset of infinite passenger seats and 1 Empty subset of seats not available for passengers.

4. Empty Sets:

When the infinite number of people leave the buses or the hotel they become empty, but they still exist.

The
paradox of Hilbert's Grand Hotel is no longer a paradox, but simply a
way to
describe something that can’t be measured and/or counted.

Does this mean that both everything and nothing fit together into one or more infinities because both the hotel and the buses are empty until they get filled? Is it possible to have something with an infinite value of nothing (empty set theory)?

The point I am trying to make is that mathematics can sometimes be like statistics where we can manipulate numbers within a mathematical model or algorithm, and according to the rules, to find the answers we are looking for. Sometimes we have to make up or discover the rules as we go along. Isn't this how mathematics and science came about in the first place? Isn't this why there are so many different theories about mathematics, statistics, Classic and sub-atomic/quantum physics?

Does this mean that both everything and nothing fit together into one or more infinities because both the hotel and the buses are empty until they get filled? Is it possible to have something with an infinite value of nothing (empty set theory)?

The point I am trying to make is that mathematics can sometimes be like statistics where we can manipulate numbers within a mathematical model or algorithm, and according to the rules, to find the answers we are looking for. Sometimes we have to make up or discover the rules as we go along. Isn't this how mathematics and science came about in the first place? Isn't this why there are so many different theories about mathematics, statistics, Classic and sub-atomic/quantum physics?

Our Universe has often been referred to as Hilbert Space...

"The
real world simply is quantum-mechanical from the start; it’s not a
quantization of some classical system. The universe is described by an
element of Hilbert space. All of our usual classical notions should be
derived from that, not the other way around. Even space itself. We
think of the space through which we move as one of the most basic and
irreducible constituents of the real world, but it might be better
thought of as an approximate notion that emerges at large distances and
low energies." (Space Emerging from Quantum Mechanics Posted
on July 18, 2016 by Sean Carroll)

Our 3, or more, Dimensional Universe

The 7 Dimensions of Everything and Nothing takes the idea of a Quantum Dimension to another level, Paradigm or Dimension. I am proposing that the idea of a Quantum Dimension is a set of conditions or properties that allow us to measure something in our reality rather than the coordinates of the object that we are measuring in a 2 or more dimensional space. Dimensions become sets of conditions or properties that pre-exist and build on each other to form our 3 (or more) dimensional reality just as length, width, and height build on each other to form something we can measure.

Our classical understanding of the properties of a set of dimensions, or coordinates, is something that can be defined and measured within our 3 (or more depending on the point of view) dimensional reality.

"The
only real defining property is that they have a length, width, and
height. If you place them on a Cartesian plane, you will have a X,Y,
and Z axis - three axes means 3 dimensions. Aside from that, 3
dimensional objects tend to be built from 2 dimensional objects that
form a “net” - a building block."
(Oct 8, 2017 What are the properties
of three dimensional shapes? - Quora)

But what if a set of Dimensions was a set of conditions or properties that allow us to measure something in our reality rather than the coordinates of the object that we are measuring in a 2 or more dimensional space? For example, we can measure something in relationship to something else (a ruler or scales) and come up with a measurement. But what are we measuring? How do we define it? What is that measurement related to? We need a standard or set of conditions to be able to make sense of that measurement in the first place before we do anything else. We can't measure it if we have nothing to compaire it to. What are the Demensions (conditions or properties) that allow us to measure something and make sense of the measurement? You will probally say length, width, and height. But where do they come from? What conditions or properties allow us to make the measurement in the first place? How can we measure something that is not within our 3 or more dimensional reality with the tools that are a part of our 3 or more dimensional reality? Its a bit like trying to take a photograph with a hammer.

"The
properties of a quantum dot are determined by size, shape, composition,
and structure. The interesting electronic properties of quantum dots
arise from the specific size of their energy band gaps. Dec 19, 2018 -
The Properties and Applications of Quantum Dots" (Dec 19, 2018 - The Properties and
Applications of Quantum Dots)

It seems to me that the idea of a Dimension takes on a whole new Paradigm (or Perspective). Dimensions become sets of conditions or properties that pre-exist and build on each other to form our 3 (or more) dimensional reality just as length, width, and height build on each other to form something we can measure.

Peter S Anderson

Perth, Western Australia