To infinity and beyond

You know you are having a quiet day when you start reading about infinity and time paradoxes. 

We all smiled at Buzz Lightyear with his 'To infinity and beyond.' I knew, as many of us did, there could not be anything beyond infinity but, of course, as with so many things, I'm wrong.

It seems there are indeed an infinity of infinities and if you want to start boggling your brain follow this link for a starter. See what I mean?

Let this blog be the seat of new learning for us all.

Then I discovered Hilbert's paradox of the Grand Hotel. 

'Hilbert's paradox of the Grand Hotel is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often. The idea was introduced by David Hilbert in1924.'

With me so far?

'Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests.' [thephilosophyforum.com]

'Another thing that can be done with this imaginary hotel is to double the number of people inside, again when all the rooms are already full. This is done by asking each guest to multiply their room number by two and move to that room. (If their previous room number was n, this time they would move to room number 2n.) This would send the guest in room 1 to room 2, the guest in room 2 to room 4, the guest in room 3 to room 6, the guest in room 4 to room 8, and so on. After finishing, we find that all the rooms with the odd numbers are empty. Then we can put an infinite number of guests into these empty rooms. Now the number of guests in the hotel has been doubled without making the hotel bigger.' [kidzsearch.com]

I bet that gives the Night Porter an added dimension to the role and what about the breakfast staff? How are they going to cope with an infinite number of breakfasts each morning? That breakfast buffet is going to be a disaster. Tips could be good though.

Apparently an infinite bus also arrives with an infinite amount of passengers wanting to stay the night. 

Where would you park an infinite bus?

So not Travel Lodge then.

This got me thinking about these different forms of infinity and time. It really is a quiet day as you can tell. I'm not a mathematician so we won't get into formulae, which is a relief to us all, but it seems to me that the philosophical issue of infinities and time needs further exploration.

I propose some new infinities or variations on perception of time and paradoxes;

Infinities

1. Waiting for a recruitment agency to reply after contacting you to say they have an urgent vacancy to fill and you fit the profile.
2. Waiting for any response to any job application.
3. Waiting for the formal rejection even though 20 weeks have passed since you had the  interview.
4. Waiting in for a courier to deliver a package. 'Delivery will be made sometime between 0730 and a time convenient only to ourselves. Please be in or you will have to collect the parcel from our distribution centre 125km distant and open from 0310 to 0325 weekdays only during months that do not have a vowel in them.'
5. Waiting to hear the outcome of an interview. 'We will contact you in 1n days.'
6. Waiting for one of your children to answer an email you've sent them [note this is an incalculable amount of time approaching 'never.']
7. Waiting for a politician giving a straight answer to a perfectly reasonable question from a journalist.
8. The train journey to my nearest city stopping at every local stop

Time

1. A journey to a holiday destination always seems to take longer than the journey home.
2. The impossibly short time between a courier knocking at the door, you running to open the door only to find the courier has left the drive, the kerb edge, the entire road, yet still managed to leave a 'sorry you we missed you card.'
3. The impossibly short time a youth leaves when walking, staring at their smart phone, looking up and then swerving to avoid you as you walk towards them.
4. The time between getting toothache and managing to book an appointment with the dentist expands in exact proportion to the pain experienced.
5. The time it takes to get through to a call centre agent when your mobile phone has a technical problem caused by them. 
6. The time it takes to explain to a mobile call centre agent that you have a) turned the phone off and on again already b) taken the SIM card out, stared at it then put it back in c) yes the software is up to date d) it's an iPhone, you can't alter the APN settings but you still can't receive phone calls.