Looking for a calculator that goes up to 40 descimal places.

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Tue Apr 27, 2004 9:07 am

Hey guys, interesting fact that having 26 letters in english alphabet you can come up with up to 29 quintillion words (thats 29 with 27 zero's). the problem is, I just found out the fact and now want to make my own assessment of the number. My rough estimation only went up to 24 * 10^35 words of up to 26 letters in length, and more than that i have still not excluded all the combinations of repeating letters(gggggggggg), and closed sound words(sqtrhk). I am looking for a calculator that will go up to about 35-40 descimal places. My friends suggestion was to write a program in c++ using setprecision(40) for the output:

Code: Select all

#include <iomanip.h>
//code for the calculations

but it's pretty hard to write in (26*1^26)+(26*2^26)+....(26*26^26)
for the calculation of the number and then subtract 26^2 for all the repeating letter words and i still have not come up with an equasion for all the complicated not sound repeating words (llleeeessssssaaaannnn)
Last edited by Alex on Wed Apr 28, 2004 4:38 pm, edited 1 time in total.

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Tue Apr 27, 2004 12:51 pm

I'd be interested to know how you're defining "word" -- it seems entirely arbitrary. The English language doesn't have any hard-and-fast rules about what a word is. There are a lot of things you could make that fit most words, but English is an evolving language and every rule you might think of has probably been broken.

But anyway, what exactly do you mean by making "your own assessment" of the number? There's not much to understand about it -- you don't really gain anything by knowing all 38 digits and mathematically speaking there's nothing unique about the number.

Concerning software, if you just want a calculator with lots of digits of precision, Microsoft's PowerToy Calculator works fine (and is nice to have around anyway) -- it goes up to 512 digits. If you want to be able to enter more complicated formulas or work with sets, matrices, and whatnot, then really the best option by far is Mathematica. It has a learning curve like Everest, but you'll never need another calculator, ever. But it'll cost ya.

But if you can come up with a clearer definition for "word", this can probably easily be done in most any programming language.


Tue Apr 27, 2004 4:38 pm

well by word i mean a speech sound or series of speech sounds that symbolize and communicate a meaning without being divisible into smaller units capable of independent use. And the number does not really mean anything at least to a lot of people, but you see what sparked my interest was a book that I'm reading (words origin book), when i got to alphabet i read an interesting article about the ammount of english words possible and just was interested in having my own estimate of the ammount of words possible in the english language. By the way, and this is what really pushed me into spending my mathclass to come up with a few formulas, did you know that if every person in the world wrote 40 pages a day with 40 english words that they have come up with, assuming that none of the words get written twice, that it will take all the population of the earth more than 1000 years to compleate a task of simply identifying all the possible combinations.
I'm not planning to remember all 38 digits, but i will have something to say when someone at a casual party starts talking about languages.
By the way, i know that the rules of grammar have been broken by a lot of words ex: to absquatulate or floccinaucinihilipilification even some of Shakespear's words like honorificabilituditatibus, the that's why I'm not excluding the words that do not abide certain rules.
and i'm not counting really long words like pneumonoultramicroscopicsilicovolcanoconiosis, because if i went up to 45 letters the estimate would be much much higher than the one i came up with. I am just talking about the possible ammount of combinations of just the 26 letters A-Z...

For the words up to 45 letters long the possble combinations number is: 1773021579913242830552281373968052041021759390

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Wed Apr 28, 2004 5:14 pm

Aaah another update, it turns out that i was wrong in my calculations... the real ammount of all the possible combinations is the factorial of 26 (1*2*3...*26) squared.
This thing is getting annoying really, but i think that i will stick with this answer: the possible ammount of words in the english language is
620,448,401,733,239,439,369,000 according to William Walsh...
The world's population is about 6,363,657,000 people. Now say that every person in the world wrote 40 pages a day with 40 words on the page, thus daily 10181851200000 words would be recorded and defined. Taking that and multiplying that by 365.25 days a year we get 3718921150800000 words recorded by the world's population this year, now from some research i've done i found out that the world's population is growing at the rate of 1.4 percent annualy. So going from there saying that our annual birth rate will go keep steady, it will take us some 166,821,000 years to write down all possible transpositions of the english alphabet...

Comments are welcome.

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