The Altera Centauri collection has been brought up to date by Darsnan. It comprises every decent scenario he's been able to find anywhere on the web, going back over 20 years.
25 themes/skins/styles are now available to members. Check the select drop-down at the bottom-left of each page.
Call To Power 2 Cradle 3+ mod in progress: https://apolyton.net/forum/other-games/call-to-power-2/ctp2-creation/9437883-making-cradle-3-fully-compatible-with-the-apolyton-edition
Well, Kuci, if you let P equal the number of Polytubbies idle enough to spend time on obscure metamathematical bastard-word-games, you discover that P is an ever-increasing quantity. As such, P might be considered "infinity." As infinity is by nature not able to be described by any number of words, well, there's your answer. Now somebody turn this into a babe thread.
Is the statement "Let n be the smallest positive integer than cannot be defined in fewer than twenty english words" a definition or a description of a definition?
The second problem is, of course, how do you define an integer with English words?
The third problem is, do you define an integer, or do you merely describe them?
(\__/) 07/07/1937 - Never forget
(='.'=) "Claims demand evidence; extraordinary claims demand extraordinary evidence." -- Carl Sagan
(")_(") "Starting the fire from within."
Why can't you be a non-conformist just like everybody else?
It's no good (from an evolutionary point of view) to have the physique of Tarzan if you have the sex drive of a philosopher. -- Michael Ruse
The Nedaverse I can accept, but not the Berzaverse. There can only be so many alternate realities. -- Elok
Originally posted by Kuciwalker
No, I think KH answered the problem correctly. There are numbers that cannot be defined in fewer than 20 words, but you can't prove it.
1. Write a number that cannot be defined in less than 20 words.
2. Attempt to describe it in less than 20 words and fail.
3. Let the others in the thread look for a way to describe it in less than 20 words, and fail.
4. Congrats, you have just proven that there are indeed figures that cannot be described in less than 20 words. That is, it is proven until someone shreds your claim with cleverness.
"I have been reading up on the universe and have come to the conclusion that the universe is a good thing." -- Dissident "I never had the need to have a boner." -- Dissident "I have never cut off my penis when I was upset over a girl." -- Dis
It doesn't even mean "not disprovable ever". "Proven" is a positive term. To prove something you must proceed from the axioms of the formal system by the deductive rules of the formal system and arrive at the statement.
It has nothing to do with Godel or incompleteness. It is all about inconsistency. All you've done is shown that a certain logical system--namely the form of naive set theory that allows such descriptions as "cannot be defined in fewer than twenty english words"--is inconsistent. Alternatively, you have proven that if set theory is consistent, then the predicate "cannot be defined in fewer than twenty english words" cannot be expressed in the language of set theory.
If you know some set theory, here's a similar paradox: Say that a set is definable if, well, we can define it in some way. There are clearly only countably many definable sets, since any description must be finite in length. Thus there exist some undefinable ordinals. Let alpha be the least undefinable ordinal. But we just defined it!
What this shows is that the concept of "definability" cannot itself be definable.
Last edited by civman2000; December 4, 2005, 21:51.
Comment