Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2022-04-04 18:37:15

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Library of Babel

The library of Babel is a library consisting of all the possible combinations from a to z,  and a few punctuations. Since this is not physically possible, the Library of Babel exists on the web.

It has every literal work ever written, being written or to be written and more.  In fact,  you can type anything in the search box and it WILL appear.  Even if it's a bunch of gibberish. I tried it too.  It even has mathisfunforum.com and CurlyBracket in it.

Brief History

The Library of Babel was a science fiction short story by Argentinian author Jorge Luis Borges which featured a library of the same name.

The Story's Wikipedia page wrote:

The majority of the books are pure gibberish, but the library also must contain, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books.

The library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages.

In 2015, Brooklyn author and coder Jonathan Basile, turned this idea into a website.

The Infinite Monkey Theorem

WARNING !!! The following information is completely in layman's terms. This is because I am a layman,  and I am explaining it.

If I give a (uneducated) monkey a typewriter and let it type for a reasonable amount of time, it is unlikely that the monkey will succeed in producing a single proper sentence.

But if I endeavor to give it an unreasonable amount of time, say...infinity, it will almost certainly produce a proper sentence.

In fact, it wouldn't be surprising if the monkey succeeds in typing the Merchant of Venice and all the contents of the MathsIsFun forum and website fifty times over.

In infinity, nothing is surprising because our instincts of what is probable and what is not breaks down completely. Because we are trained to be practical and reasonable, and unreasonable time scale are too complex for our intuition.

The Website

Library of Babel

Last edited by CurlyBracket (2022-05-17 21:39:59)


Learning is fun - Exceptio probat regulam!

Offline

#2 2022-04-04 19:44:04

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

hi Curlybracket

That's an interesting discovery.  As it has infinite storage, perhaps we can all use it for cloud memory.

But I checked and "the library of babel does not exist" is in the library.  If only someone could come up with a way of sorting the true statements from the false.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#3 2022-04-06 00:31:42

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Hi Bob,

As it has infinite storage, perhaps we can all use it for cloud memory.

Good idea, but a little difficult to execute! I'm still trying to understand how to navigate the library.

If only someone could come up with a way of sorting the true statements from the false.

Speaking of seperating the truth from the false information, did you know that someone I know actually invented a lie detector to be used by the police? I wonder how that works.

And also, with a little more context, I think the number of false statements will be much greater than true statements, isn't it?

The truth is rigid, and can only be true if everything is factual.

The fake is flexible.

For example, "The sun rises in the east."

This simple truth can have various falso variations, ranging from the sun rises in the west, to the sun doesn't rise at all!


Learning is fun - Exceptio probat regulam!

Offline

#4 2022-04-06 20:25:34

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

I'll make the following conjectures:

(1) The set of true facts in the library is 'countable'. (infinite aleph-nought)

(2) The set of false facts isn't countable. (infinite aleph-one)

https://en.wikipedia.org/wiki/Aleph_number#Aleph-one

At this stage I haven't a proof for either.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#5 2022-04-30 18:36:04

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Yes, I agree.

But the factor of place, time, and even a reader can further complicate the 'truthfulness' of a statement.

Again, here's an example:

"I'm bob bundy."

Here, if you're the reader, then this statement is true.

But if anyone else reads this, it's false.

"Today is the first of May."

True for today, but from tomorrow, it's false.

"I live in the financial capital"

Might be true for a person who does live in the financial capital, but not for someone who doesn't.

So even how true a sentence or paragraph is oftentimes changes from person to person.

The truth is also flexible!


Learning is fun - Exceptio probat regulam!

Offline

#6 2022-04-30 20:32:42

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

'Facts' like these  become provable (or not) only when we know the context of the fact. If the statement includes a declaration as to who is making the statement as in Bob says: "I am Bob" then we have a way of testing the truth or otherwise. The library will have such statements, and a lot more where we don't know the context.  The truth of those cannot be determined.  Schrodinger's cat and trees that crash silently in empty woods fall into this category.

Fortunately, the world keeps turning nevertheless. 

"What we demand," said Grunfondle, "is rigidly defined areas of doubt and uncertainty." (Hitchhiker's Guide, Douglas Adams)

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#7 2022-05-01 16:43:46

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Does that mean that a statement is both true as well as false simultaneously, until it has been read by a specific person under specific circumstances?

I have heard of Schrödinger's cat.

If I understand rightly, the cat is both alive and dead until someone checks on it.

But what do falling trees have to do with it?

...rigidly defined areas of doubt and uncertainty.

Wow... that's as confounding as my "Exeptio probat regulam".


Learning is fun - Exceptio probat regulam!

Offline

#8 2022-05-01 19:37:29

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

There's an ancient philosophical question: If a tree falls in the forest and there's no one around to hear it fall, does it make a sound?

The doubt and uncertainty comes from 'The Hitch Hiker's Guide to the Galaxy' by Douglas Adams.  If you haven't read it I heartily recommend you put that right straight away.  It's very funny.  There is also a film and two BBC series, TV and Radio. You will also learn the ultimate answer to the questions about life, the universe and well, everything.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#9 2022-05-01 21:35:20

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

If a tree falls in the forest and there's no one around to hear it fall, does it make a sound?

Ah, yes. I remember reading something along those lines in my 7th grade textbook.

It was explained most naturally by the authors, by saying that philosphers, having a tendency to be subjective, believed it will not produce any sound, while scientific people instisted it will. But now this is an important question in both fields. Is the rigid line finnally blurring?

This is the first time I have heard of The Hitch Hiker's guide to the Galaxy. It sounds interesting. I'll surely try to get my hands on a copy.

But the bit about Life, the Universe and Everything...did you make that up? Because it sounds oddly like the description of the Dark Discussions Forum.


Learning is fun - Exceptio probat regulam!

Offline

#10 2022-05-10 05:13:41

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Hi,

I was thinking about this today, and I came to the conclusion that the idea of "cleaning up the false statements" is impossible.

I'll try to explain my logic the best I can.

Let's say I assign a person with the mammoth task of clearing up the false statements.

Then the Library of Babel, will be completely right, but only for that person at that particular moment.

Then an absolutely correct Library will have to be constructed for every single person who was, is and will be in existence, and it has to be updated every second.

For example:

Before this thread, I didn't know anything about the Hitch Hiker's Guide to the Galaxy.

So from my perspective, it did not exist.

But after ward, I learnt of it's existence, making it false.

This makes Bob's "The Library of Babel does not exist." also exist in a state of duality. Before reading this thread, it is possible that this sentence would have been perceived to be true by many, and false after reading.

So what if I write something like:

"XYZ, living in (address) did not believe in the existence of the Library of Babel, as precisely (time, date)"?

There is a possibility of there being another fellow of the same particulars, if not in this universe, then perhaps in another.

After all, in this discussion, we assume the same idea as good old Schrödinger, that each simple choice we make generates a whole new universe, where the other choice(s) have been selected.

What do you think?

P.S. My sincere regards to any one who has has the patience to read through this jumbled pile of a post.


Learning is fun - Exceptio probat regulam!

Offline

#11 2022-05-10 23:11:05

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

hi

This guy is going to have difficulty clearing up all false statements.

Consider the statement "This statement is FALSE".

At first sight is seems easy to deal with; after all it's telling you it's false so it's got to go hasn't it?

But let's just think about it. It's a statement, so it is either TRUE or FALSE. 

Let's try them both.

Assume it is TRUE.  In that case it shouldn't be cleared out as we're only after the FALSE ones.  But if TRUE, it is TRUE that it is FALSE, so we have a contradiction.

Better try assuming it is FALSE.  If it's FALSE then the statement is lying when it says it is FALSE, so it must be TRUE. Once again we have got a contradiction. dizzy

Once you get the hang of it, you can make up loads of statements like this.

The Hitchhikers Guide to the Galaxy started out as a BBC radio series.  Then there was the book; then a TV series and finally a full length film.

It acquired a cult following when it first happened on radio and fans loyally claim that the radio version is best.  Personally, I think the TV version is better; it has all the action and sound effects plus fantastic graphics illustrating the Guide itself. I should explain, the Guide is an electronic book containing loads of helpful advice for the hitch hiking space traveller, like where to get the best drinks and how to get a ride on a Vogan spaceship. It also has the helpful advice on the cover "Don't Panic".

I've checked and a popular on-line company has copies in all formats.

Douglas Adams followed it up with 4 more books in the Trilogy (no error!).  I didn't find them so funny ... the original was delightfully different and full of zany ideas ... but there's only so many times you can tell the same joke.  If you like it, Adams also wrote two detective novels starring Dirk Gently, and these are equally wonderful (IMHO).

The question about Life, The Universe and Everything comes from the book and helps explain lots of things that puzzle the average human. You will also get the answer to this important question, but you probably won't like it.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#12 2022-05-11 18:43:21

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Hi,

Ah, yes, the self-referential paradoxes. How could I forget?

I once specialized in confounding people at school with my bag of paradoxes.

I remember another of the same line, "A Trojan said, "All Trojans are liars." Is the Trojan lying?"

I definitely would avoid being the clean up guy if I could help it.

Bob wrote:

I should explain, the Guide is an electronic book containing loads of helpful advice for the hitch hiking space traveller, like where to get the best drinks and how to get a ride on a Vogan spaceship. It also has the helpful advice on the cover "Don't Panic".

Sounds like the best Guide ever. I wish every Guide said "Don't Panic." I'd probably panic more and cancel the trip, but no one can say the Guide didn't do its job.

But, by your words, it appears that it's a well known book, and yet it is completely new to me. Was it popular quite a few years ago?

Douglas Adams followed it up with 4 more books in the Trilogy (no error!).  I didn't find them so funny ... the original was delightfully different and full of zany ideas ... but there's only so many times you can tell the same joke.  If you like it, Adams also wrote two detective novels starring Dirk Gently, and these are equally wonderful (IMHO).

That's a lot of books. Looks like I have my next few vacations sorted smile

The question about Life, The Universe and Everything comes from the book and helps explain lots of things that puzzle the average human.

A book with the answer to Life, the Universe and Everything? And I won't like the answer? What is it, 42? big_smile


Learning is fun - Exceptio probat regulam!

Offline

#13 2022-05-11 19:20:22

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

The answer 42 first came from the book so it seems you have, without realising it, encountered THGTTG already.  The Guide is certainly VERY useful; it saves Arthur Dent's life several times.  Enjoy!

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#14 2022-05-11 20:47:49

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Wait...it is 42?

My friends and I use it all the time as a form of a joke. It's a funny way of saying "I don't know" to a question. You'll notice that I've used the number in the same way in my previous post.

To think it came from a book!


Learning is fun - Exceptio probat regulam!

Offline

#15 2022-05-12 19:19:22

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

There is another way to get the book of course, and that's to read it in the library.  It is certainly there!

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#16 2022-05-17 02:20:52

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Library of Babel

Hey guys,
I really enjoy the nice little philosophical discussion that's revving up around here... although a real life Library of Babel might as well be nonexistent as with all the great fables of literature, one may access a virtual, online library of Babel(which also has an analogous image repository). All the solutions in the world, in one online repository...


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Offline

#17 2022-05-17 18:40:43

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Hi Mathegocart,

I remember adding a link to the website at the end of Post #1, but it seems to have disappeared. Thanks for mentioning it here!

Yes, a real life LOB would be incredibly impractical. I shouldn't be surprised if it doesn't fit in the area of Russia, with each building being the height of the Burj Khalifa.

All hail the Internet!


Learning is fun - Exceptio probat regulam!

Offline

#18 2022-05-17 19:58:54

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

You did have a link in post #1.

I've no idea why it has gone.  Perhaps you could try editing it back.

When someone puts a link into a post I check it out just in case it's not 'wholesome'.  Quite a few spammers have gotten banned because of that.  The library looks ok to me; I've rechecked it today.

They say that if you search for a particular book on a specific shelf and note its contents; you'll get the same if you repeat that another day.  So it is not just generating random characters.  Must check that out and see if Shakespeare is in there.  I discovered today that there is an image library as well.  Hhmm.  Wonder if my mugshot is there?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#19 2022-05-17 21:50:15

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Last edited by CurlyBracket (2022-05-17 22:15:00)


Learning is fun - Exceptio probat regulam!

Offline

#20 2022-05-17 22:27:01

CurlyBracket
Member
From: Your Maths Textbook
Registered: 2022-01-03
Posts: 140

Re: Library of Babel

Hi,

I'm not sure what the matter with the reply above is.

To read the post, consider click on Quote.

I wonder if there's a certain number of characters which the forum can allow in a single post?

The post was ok before, but I decided to put the image numbers in hide tags to facilitate scrolling, and then this happened.

Last edited by CurlyBracket (2022-05-18 04:12:47)


Learning is fun - Exceptio probat regulam!

Offline

#21 2022-06-16 10:03:29

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Library of Babel

I had an interesting thought: if the library of babel contains all books of a certain length, then could find solutions to everything (i.e. current world problems, unsolved problems in math like the collatz and goldbach conjecture and p vs np) by searching for relevant text, filtering out the books with nonsense, and using some method to find the solutions that work?


pi³

Offline

#22 2022-06-16 19:15:57

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

But, as well as containing all the proofs to unsolved maths problems, it'll also have all the false proofs, and there'll be a lot more of those!

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#23 2022-06-17 11:50:12

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Library of Babel

In theory you could create a program that validates proofs


pi³

Offline

#24 2022-06-18 02:09:11

Bob
Administrator
Registered: 2010-06-20
Posts: 9,583

Re: Library of Babel

I think you could.  My 'Mycroft' has been working on this sort of thing since he graduated.  Try googling the School of Informatics,  University of Edinburgh.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#25 2022-06-18 19:37:32

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Library of Babel

Bob wrote:

I think you could.  My 'Mycroft' has been working on this sort of thing since he graduated.  Try googling the School of Informatics,  University of Edinburgh.

Bob

I've got the university, but what specifically are you referring to?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Offline

Board footer

Powered by FluxBB