The Berry Number

[Ghost Post]

Being a mathematician, I loved this puzzle. But, its not a problem for numbers to solve, its for the philosophers of language. A reading of Derrida would help anyone confused with this essential idea: language is self-referential, and limitless in its capacity to to create definitive pointers to larger linguistic constructs. The 'Berry Number' puzzle is a hoax; for a solution it asks for a limit to something who's primary quality is to be unlimited. The puzzle is not a paradox, nor does it hint at one; and I feel sorry for Bertrand, he would have appreciated the philosophy of the last century.

[tv snake]

What do you mean by unlimited?

2 to the power of 3 to the power of 4 to the power of 5 to the power of 6 to the power of 7 to the power of 8 to the power of 9 to the power of 10 to the power of 11 to the power of 12 to the power of 13 to the power of 14 to the power of 15 to the power of 16 to the power of 17 to the power of 18 to the power of 19 to the power of 10 to the power of 20 to the power of 21

Is a number that cannot be expressed in 100 words or less. Yet it is not unlimited because it has a value.

[Ghost Post]

Language is limitless, not a number in twohundred words or less. The primary quality of an active language is to create words/symbols/definitions for emperical subjects. In its capacity to do this, language is infinate. As the original puzzle implies: it is alway possible to form a definition in less than two hundred words, then give it a name. Every new name would embody a larger concept, thus giving more room and words for a broader concept, or in this case, a larger number. A good analogy for this is the concept of the 'pointer' in object oriented programming.
This quality of language, its dynamic ability, its self-reflexive nature, has always facinated me. Some great books and stories come to mind: Godel, Esher, Back; Asimov's short story of a NOVAC, the supercomputer, which stores all information until the etropometic end of the universe, then answers the ultimate quesiton in another Big Bang; the philosophy of Jaques Derrida (how I got his name right); and the famous Godel theorem. I can't help wondering which came first: consciousness or language.
As you can see, the puzzle has nothing to do with finding an actual number. The largest number recognized to exist is a google. It dosn't mean we can not use the rules of mathmatics to sybolize larger ones; google is simply where mathemeticians have desided to draw the line knowing there would otherwise be no end. Also note that the concept of infinity is just that: a concept. Its useful in number theory and limit applications, but not to quanitize anything. Thank you for your reply.

[tv snake]

Ok, you're talking about the definitions of the numbers... your point is a good one. There's a thread in Off Topic that took the Berry Number concept a bit too far... they ended up with "The product of all the numbers in this thread" and the like...

If we change the puzzle so it reads: The Berry Number is 'the lowest number that cannot be described in one hundred words (from Oxford English Dictionary ed. 5) or less, without repeating any words', does this alter your opinion on the paradox? Does you're argument apply when your language is limited?

The way I read the puzzle, there is no valid proof that such a number even exists. Does it mean that the number 1 is the Berry Number? It can be expressed as "one + zero + zero + zero +....", so this must make it the lowest positive integer (is it positive integer? I'll have to check the puzzle again), and I can;t express it in 100 words in this way...

[Ghost Post]

Yes, I believe it would be interesting to limit the puzzle to a set of words and symbols, and ask what the smallest and/or largest number could be made with a specified amount of use. It would be nessisary to state that a single digit constituted one word toward the limit, or people would list a very long number and call it singular. I would be interested in peoples constructs of ten or fifteen symblos/digits/words; answers of approximatly two-hundred words were given by people who attempted the origional puzzle without considering the self-reflexive nature of language. I enjoy those attempts, and had some fun dreaming up my own, but I belive the origional intent of the puzzle was to get the reader to ponder the qualities of language I have outlined above. It is remarkable that withing two hundred words, a system may be described to interpret a truncated datum. Its likened to encription. A group of researchers called the MARU foundation treated the first twenty seven letters of the Torah as a code for unraveling the rest of the ancient text. Science fiction plots were spun off the idea, but what the actual researchers found would blow anybody's mind. Again, I belive the original puzzle was written to hint at the impossibility of finding such a number because of the nature of language, but I think it a worthy puzzle to find the smallest number within ten words and symbols recognized by mathematics and the Oxford dictionary. An answer to such a puzzle would ought to be straight forward and singular; it is not the intention to trick or mislead the thinker, but rather to apply the rules of mathmatics in the most ingenious way. Without much thought, I submit 9^-9999999 as a starting point. Note that this number is 1 over 9 to the 9,999,999th power- a very small number! And the answer uses exactly eight digits and two symbols, ten total. Also note that we are looking for the smallest number, and not the least number; negative numbers are not the game.
Can you or anyone who might read this come up with a way of wording such a modified Barry Number puzzle to make it as interesting and challenging as possible? I thank you for your responce.