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 apples were in a barrel of oranges, how many
would you say? If you said “0” or “None” does that mean that 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.

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.

If I asked you how many apples were in a barrel of oranges, how many would you say? If you said “0” or “None” does that mean that apples don’t exist (The 7 Dimensions of Everything and Nothing)?

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 hasn’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.

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 three different types of infinite sets...

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

**1.
****Unmeasurable
Sets:**
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.
****Uncountable
Sets:**
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.
****Empty
Sets:**The
hotel is a set that contains 1 set of infinite rooms and 1 Empty set of
rooms not available for guests. The infinite number of buses each
contain 1
set of infinite seats and 1 Empty set of seats not available for
passengers. When the
infinite number of people leave the hotel or the buses they become
empty, but they still exist.