The Berry Number

[ewan]

the berry number is the lowest integer that cannot be discribed with less than 200 words

a paradox? well certainly in my phrasing of the problem it is a self contradiction. but even assuming a better sentance structure I dont think its a paradox.

For this trick I will be postulating a race of strange aliens. the aliens have developed maths and understand integers, however they have a very small vocabulary which consitsts of ten digits 0-9 and three words 'the' 'berry' 'number'

now one mathematiction telepaths a thought to another, 'what is the smallest integer we can discribe with our strange laungue using only three words? lets call that number "the berry number"'

the other matematician bends his mighty brain to the problem. first he uses the ten digits and gets 1000 combinations then he intermingles the three words with digits to get (oh i cant be bothered to do the math) some more numbers, finaly he uses all the combinations of the 3 words to get 27 more combinations. 'ah hah' he thinks 'now all i need do is add one to this number and that shall be the berry number!'

Now 'the berry number' is allready assigned to 'the berry number' -1 thus it is an ambiguous name and hence dosnt specify a single integer. hence you can call this unsayable in 3 words number the berry number and not have a paradox.


of couse with a real lanugage you can just invent new and longer words

[Tom]

I'm confused.

How does he telepathise (?) across 'what is the smallest integer we can discribe with our strange laungue using only three words? lets call that number "the berry number"'; half these words aren't in his language. Or does he just get the concept across? Ok, let's suppose he does.

How does he get 1000 combinations from 10 digits? Presumably things like "17" aren't in his language, as it only has 0 to 9 and "the", "berry" and "number". If you allow "17", you allow all integers (unless you are only allowed to use each digit once, when you get up to 9876543210 with lots of gaps. But the possibilities are still 10!, which is a lot bigger than 1000).

Then he adds in the words? What does, say, "2 berry the" mean?

I suppose he can add 1 to an integer, but he can't describe it, as he has no "+" in his language, or the means to define it.

And I don't understand why "'the berry number' is allready assigned to 'the berry number' -1".

I'm very confused.

[ewan]

tom:

1:OK when these aliens use telepathy they comunicate without words in a direct mind to mind exchange of ideas (this is why thier lanuguage is so limited)

2: he gets 1000 combinations because he has 10 words 1,2,3,4,5,6,7,8,9,0 and three slots to put them in, there are no words like tweleve or twentyseven they mearly say "1 2." or "2 7." (infact now that I think about it he could get more than 1000 since lack of a word is a choice "2 7." is different from "0 2 7."

3: "2 berry the" would corrospond to some number after you had run out of all the combinations of digits. for example say you run out of digit combinations at 999, you could represent 1000 with "1 berry" etc

4: he can add one to an integer since othey are a very advanced mathematical race, howver hes cant _say_ "add one to 45" since none of these words exist.

5: imagine you are counting in binary, you effectivly have 2 words you can say, "on" and "off" and you are limited to saying only two words at a time. But you can count to 4 by using combinations of these two words, eg. "on on" = 4 the aliens are effectivly counting in base 13 limited to 3 digits (with some extra numbers using only 2 or 1 word) since they try all the possible combinations of words "the berry number" will corrospond to some number, say 2563, hence w2hen they get to the limit of the integers that they can count to with only 3 digits they add one and call that number "the berry number" but hang on... isnt "the berry number" allready = 2563? hence "the berry number" is ambiguous

[Tom]

Why can they only use 3 words for a number?

[Mercuria]

something about three word digits...

[CrystyB]

Ewan, what's your problem? Have you something to ask? When and where are you going to ASK it???

[azu]

is "the berry number" part of the english vocabulary?if no then the number which can not be named with less than two hundred words (which we thus call the berry number,)can still not be perscribed in less than two hundred words.If it does belong to the english vocabulary ,should we accept that the berry number is that which cannot not be otherwise expplained in less than 200 words(without the use of the phrase "berry number")?does this not make this number unique?

/

[What if...]

I agree with azu that the only way to have an actual berry number is to exclude the use of the phrase "berry number" from the description of the number itself, as the berry number is supposedly the three word name for a concept requiring 200 words to express. I'm not sure what Ewan's trying to say? The alien can just decide not to use the number "the berry number" until the end, so it has not already been used for a lower number. Also, the berry number in the usual sense is the lowest number that must be expressed in 201 or more words, not the highest needing less than some number of words. Also, you use a natural number, rather than an integer, because there are really big negative numbers that would technically be lower than anything you could describe in any number of words you chose, and so the berry number's value would go to negative infintity.

[cha]

So what are some possibilties for this number? If one hundred and twenty one" is considered 5 words, and "one hundred and twenty one thousand (million, billion...)" is six words, then a possible Berry would be:
21,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,
121,121,121,121,121,121,121,121,121,121,121,121,121,121,121.
Written and spoken this way, wouldn't this number use 200 words?
Of course, this could be written 2.1121121121121... x 10 to the whatever, which when spoken, comes to 110 or so words.
So what about 1.1111... x 10 to the whatever it takes to come out to 200 words?
Or maybe I shouldn't drink and do math.

[What if...]

I think finding an actual berry number would simply require two things:
1. The series of words which describes the largest order of magnitude divided by number of words number (no operations performed)
2. The operation which increases a number the most orders of magnitude divided by number of words it requires.
If you find something else, post it...