The city of Lise’s counterpart, Rózsa is constructed entirely out of numbers. While Lise saw words as the foundation of human existence Rózsa instead saw numbers as this foundation. In numbers Rózsa’s residents saw an infallible source of information based on the solid principles of logic and reason, unchanging in value.
Just as Lise took words from books and the air, Rózsa took numbers from the same sources. Numbers were taken from maths books, signs and were trapped from the ether. Numbers were written on empty sheets of paper and then taken from the paper. After amassing enough numbers the city of Rózsa was constructed of numerical forms.
In the beginning the city of numbers worked exceptionally well. With numerical values appearing to be fixed the city remained constant, never wavering. The largest numbers comprised the foundations of the city as well as the infrastructure and sewer systems. They were also employed in the construction of tall towers. The suburbs were mad up of smaller, safer numbers and centres of learning and commerce were built with complex numbers containing decimal points and other such characteristics.
Building the city was easy, as is making additions to it. Making bigger buildings is simply a case of adding two smaller numbers together. In a similar way buildings can be multiplied, divided and if needed subtracted. Everything in the city of Rózsa was working well.
Up until now. Rózsa’s scholars have found something that was overlooked when constructing Rózsa. Kurt Gödel’s Incompleteness Theorem. It states that
1) A consistent system cannot be complete
2) The consistency of the axioms in the system cannot be proven.
Despite Rózsa’s best attempts to create a city of perfect order Rózsa now realised that their system of construction had to be incomplete meaning that all the values in the system could never have consistent values. And without the construction materials having approximate values Rózsa finds itself in a position were it is unable to grow and what has already been build is in a state of flux. Research has shown that the use of infinite cardinals may fix this problem but as human beings cannot comprehend infinity the use of these cardinals could have untold consequences.
In its search for logic, order and reason Rózsa finds itself trapped in a world of uncertainty and paranoia as the supposedly infallible system of numbers has been revealed to have cavernous faults.
The name of the city comes from the mathematician Rózsa Peter: http://en.wikipedia.org/wiki/R%C3%B3zsa_P%C3%A9ter
If anyone with a mathematics background reads this could you please let me know if I have used Kurt Gödel’s theorem correctly. I do not have in-depth knowledge of advanced mathematics so any feedback on this would be appreciated, as well as on the text as a whole.
Kurt Gödel’s Wikipedia page: http://en.wikipedia.org/wiki/Kurt_G%C3%B6del
Cardinal idea inspired by an article in New Scientist.