The hotel at the end of the universe
The roomiverse is infinite.
The policy of the hotel at the end of the universe (owned by the Zake Busybod Foundation) is to build two new rooms for every one that people come to fill.
Zake’s business partner, Harry, decides to go into business for himself and builds another infinite hotel, but even bigger than the original. Nonetheless, he wonders how it might be done. His manager suggests that they should divide the rooms in half each time.
Harry then advertises that his infinite hotel has twice as many rooms as Zake’s infinite hotel. Zake isn’t pleased and decides to take the matter up with the Advertising Standards Council.
The questions are who is right and what should the ASC rule?
I assume that this is all about divergent vs. convergent series. Zake’s approach is divergent, while Harry’s is convergent. The problem for Harry is that his rooms will rapidly become too small to accommodate guests. Either way, there’s still infinity to be had.
The discussion in the book mentions Georg Cantor and different types of the infinite – that which has no bounds (Zake’s infinite hotel) and that which is bounded (Harry’s hotel).
Zake’s business partner, Harry, decides to go into business for himself and builds another infinite hotel, but even bigger than the original. Nonetheless, he wonders how it might be done. His manager suggests that they should divide the rooms in half each time.
Harry then advertises that his infinite hotel has twice as many rooms as Zake’s infinite hotel. Zake isn’t pleased and decides to take the matter up with the Advertising Standards Council.
The questions are who is right and what should the ASC rule?
I assume that this is all about divergent vs. convergent series. Zake’s approach is divergent, while Harry’s is convergent. The problem for Harry is that his rooms will rapidly become too small to accommodate guests. Either way, there’s still infinity to be had.
The discussion in the book mentions Georg Cantor and different types of the infinite – that which has no bounds (Zake’s infinite hotel) and that which is bounded (Harry’s hotel).
Tomorrow, we embark on some of Zeno’s paradoxes and I may have to use the word “calculus”. Oh dear.
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