I've decided to re-post some musings on the concept of infinity, that got wiped in 'the great crash' of twenty ten.
My feelings are infinity fundamentally cannot be accurately conceptualised, fully envisaged or grasped, as rather it appears representative of that in which conceptualisation itself
takes place. It's described as having certain qualities including; being endless and beginningness, so eternal in a sense. It tends to conjure images of being vast but could also be thought of as having no dimension at all, perhaps due to the nature of scalar quantification. An analogy would be that it is the canvas on which mathematics takes place, the space, the emptiness of inherent existence. Source. God if you like. It is not really an it at all. It merely Is. God...IS...infinite.
The error appears to be in conceiving it as not inherently existing, combined with the objectification of unit(s).
I should probably add here that I'm no mathematician, I have only the most basic education in a subject in which I did not excel, and frankly cannot even recite the 6 times table. As a child when my father tried to teach me that 1 +1 = 2, I demanded to know why. 'It just is' was the reply, and after some persistence on my behalf it became apparent that such things needed to just be accepted as a matter of convention ..... at that stage anyways. The upshot being, I fast lost interest.
I do enjoy abstract thinking though, and could go a fair way to envisaging why the universe might be described as a 4-dimensional donut in some quarters, hehe.
Firstly a brief look at the world of large numbers for some 'scale';
In every day life most people only encounter numbers up to....say, millions... or billions, ...... occasionally trillions maybe. However In the world of numbers these are tiny.
- is 1 followed by 100, 0's
Does not sound that big ?..... It is greater than the total amount of atoms in the human body, greater than the number of atoms that make up the Earth, in fact it is greater than all the atoms in the entire observable universe .Yet it is a very, very, very tiny 'large number'
- is 1 followed by a google of 0's
This number is so large that there would not be enough room to write it down even if you could fit a 0 on every atom in the entire observable universe as per above. You can see how comparison might start to become difficult here yet this number is still very small.
(officially the largest number) - is the upper limit to a solution to a mainly abstract mathematical problem concerning multi-dimensional cubes.
It is as large to a googleplex as a googleplex is to the number 10. In fact it is much bigger than that. It is so large that no-one knows how many digits it has, what number it starts with, or even if there are more 1's than 0's (yes even Graham!!)
It requires a lengthy calculation just to reveal the last number (which incidentally is 7). So Graham's number is a finite number, yet it cannot be fully comprehended.
Incidentally the methods used to make the calculation are now employed to keep track of internet traffic - one of its few practical applications.
........The problem is that it would still take infinitely more calculations to reach infinity.
Infinity has some strange properties; It never comes to an end.
The list of even numbers is as long as the list of even plus odd numbers combined even though there appear to be half as many. This is because we are counting, which is matching things up, and all the numbers can be matched......... So 2 infinite lists are the same length even if one appears to contain half as many numbers.
An analogy - The hotel infinity
Question. If you tried to book into a hotel that had infinitely many rooms, but was fully booked, could you get a room ?
note. You cannot check into the last room because there is no last room, and even if there was, somebody would be in it..... because the hotel is fully booked, lol.
Answer = Yes
Suggest to the manager that he asks the guest from room 1 to move to room 2, then the guest from room 2 to room 3, and so on
Then you could have room 1 and everyone else can also be accommodated because....... 'there is always another room'.
This apparently demonstrates that; infinity plus 1 (or even plus 2 or 3... whatever) = infinity.
Now, imagine that you tried to book into the hotel with infinitely many of your friends.
Could you all get a room ?
Suggest to the manager that he asks the guest from room 1 to move to room 2, room 2 to room 4, room 4 to room 8, and so on.
This would free up all the odd numbered rooms for you and your infinite amount of (probably odd) friends.
This apparently demonstrates that infinity plus infinity = infinity
Ok new question. Do the same rules apply when you divide or subtract from infinity ?
Answer = No
If all the guests left then infinity minus infinity = 0
If all the guests left but you stayed on then infinity minus infinity = 1
.......So there appears to be a discrepancy.
Infinity is like a landscape where you do maths. It's paradoxical properties make some mathematicians uncomfortable. They say that infinity is abstract nonsense that does not exist, that there is a largest number that to which if you add 1, then goes back to 0.
I don't resonate with that idea personally, I think numbers are infinite because you can always add 1, so infinity is shown to be part of an abstract reality which may be additionally the base of consciousness and ultimately awareness. The aware space or the awareness that is aware of itself.
If we go on to consider an infinite 'universe'
things become truly bizarre, but I've rambled for long enough.
Thanks for listening.