Have creatives "done everything before"? NO!: a combinatorial approach

Here's a crazy idea you Steemers will probably really enjoy

It's easy to feel overwhelmed by the collective creative output of humanity over
the last two thousand years. So much has been said, written, drawn, painted,.
sculpted, sung, played, etc, that it's easy to feel that most of what could be
expressed has already been expressed and that only variations upon universal
themes remain.

The purpose of this essay is to show that the phrase "it's all been done before"
is not even close to the truth, that there are vast unexplored realms of
creative endeavour. However, the manner in which I attempt this may be one which
is at odds with most "creative types"; by appealing to combinatorics, a branch
of mathematics.

Already a number of objections may be forming themselves in some reader's minds:
"What has mathematics got to do with creativity?" "How can you quantify creative
output?" "I hate maths, so I'm giving up on reading this now."

I'll try really hard to answer all of those questions. As for the level of
mathematics I'm going to be using, I'll only be assuming the most basic of
everyday maths. In particular there will be no calculus, no algebra, not even
fractions. If you can multiply two numbers together you're more than qualified
to keep reading.

In the early 20th century an Argentinian writer called Jorge Louis Borges wrote a
short story about a fictional library known as the Library of Babel. It was a
truly remarkable place. Each floor of the library was constructed just like
every other. Each shelf contained the same number of books as any other, and
there were a uniform number of shelves per floor. Further, each book had exactly
four hundred pages but was limited to a fixed set of letters and punctuation.
(Assume no obvious shortage of punctuation. All our familiar friends, the comma,
the period, quotes, semicolons and colons, the space are there.) As to how many
floors the library contained, no one really knew. They just knew there were a
lot.

The Library of Babel had one very special attribute: it contained exactly one
copy of every possible book of four hundred pages. No two books in the library
were the same, but there was one of every possible book. But what exactly does
the phrase "one of every possible book" mean? It may not be immediately obvious
so I'll illustrate with a much simpler example.

Let's assume that we have an alphabet containing only the (capital) letters 'A',
'B' and 'C' and that there is no punctuation. Further, let us assume that a
"book" consists of only two letters. (A very short book indeed!). Then all the
possible "books" are:

1. AA
2. AB
3. AC
4. BA
5. BB
6. BC
7. CA
8. CB
9. CC

There simply are no more "books". Can you think of one? You shouldn't be able
to.

Now imagine this on a much grander scale. Book 1, in the Library of Babel, is
the book containing only the letter "A" (with no other punctuation). Book 2, is
the book containing only the letter "A" up until the last letter which is a "B".
And so on. It doesn't really matter how you count them. What matters is that
only one copy of each possible book exists.

It's immediately obvious that most of the books are complete rubbish. Most books
make absolutely no sense. They are filled with essentially (though not actually)
random sequences of letters and punctuation. However, were you to browse this
library, you would eventually come across a book written in perfect English with
no grammatical or spelling mistakes. (Whether the book was any good or not is
another story and outside the scope of this essay.)

Even if each word is spelt correctly and the grammar of the sentence is perfect,
you can still end up with nonsense such as "Blue cow migrates prettily
underwater." Nevertheless, a fraction of those books will make sense.

Just how many books are there?

Let's say there are 26 letters in the alphabet, 10 digits, plus a few extra
exotic foreign characters, umlauts, accents, diacritics, etc. Then add in the
capital versions of these letters followed by some
punctuation marks. If we assume 26 letters, 20 foreign letters and, say, 20
punctuation marks that gives us (26 + 20) x 2 + 10 + 20 = 122 symbols. Let's
just round that up to 150 to be sure.

Now let's say there are 80 symbols per line and 40 lines per page. We can now
calculate the number of possible books of 400 pages that there are. It is:

150^(400 x 80 x 40)

Here some interesting facts about this number.

First, just writing this number down would take up more space than this essay;
much more space. The number itself is over 2.5 million digits long. If we were
to write it down it wouldn't even fit in a book from the Library of Babel. It
would take two and a bit.

Second, this number is vastly larger than the number of atoms in the observable
universe. The implication is astounding. Books are made of matter. Matter is
made up of atoms. There are less atoms than the number of possible books.
Therefore, there is not enough matter in the observable universe for one copy of
each possible book to exist.

How much bigger is the number of possible books compared to the number of atoms
in the observable universe? Call the former B (for Babel) and the latter A (for
Atom). Number A is about 100 digits long, as compared to over 2.5 million digits
for B. You would need to multiply A with itself over 26000 times to get a number
bigger than B.

Let's put it another way. Say you had god-like powers and could, at a whim,
replace every atom in the universe with a number of atoms equal to A. You would
need to do this over 26000 times to have one atom for each possible book in
the Library of Babel. Further, you need a lot more than one atom to create
a book.

So when I say that B is big, I mean it's really big.

But it's not infinite, it's massive but finite

The fascinating thing about B is that, although truly massive, it is not
infinite. It's common to see the word "infinite" used very casually in
conversation. However, I worry that many people might actually take it
literally. Say you read the following passage: "She put down a blank page in
front of her. What would she write? The page held infinite possibilities!".
Although it has a certain intuitive appeal we now know that the author really
means "massive but finite possibilities".

Wait, doesn't this mean I could read all possible books given enough time?

Immortality, should we ever achieve it, has some pitfalls. You could read every
possible book in the Library of Babel given enough time. I find this utterly
fascinating.

But for us mere mortals I wouldn't worry about it. It's estimated that the
average person can read about 1500 books in their lifetime. However, for fun,
let's assume that you're a speed reader and can read a book in an hour. Then
you could read B books in B hours.

The age of the universe (in hours) is not even close to B. The age of the
universe is estimated at around 13 billion years which is approximately equal to
10^14 hours. To put it another way, if you could replace each hour with the
number of hours that has already passed since the universe began you'd have to
do this about 185,000 times to have enough hours to speed read each book.
You'd really have to take advantage of that immortality to achieve this feat!

What about books longer than 400 pages?

The four hundred page limit is not a practical limit. Since you can imagine
"volume 2" it also exists in the library. Thus, there are books of practically
unbounded length in the library. Not actually unbounded mind you. Just
practically.

What kinds of books are in there?

• take any of your favourite novels and throw in a fake ending, or an extra
  chapter, or change all the character names but leave the book the same. All
  of these books are still in the library.

• the ramblings of a madman

• all prose written by four year olds

• every catalogue of every store around the world

• if you can dream it up, it exists!

• This essay is in there, translated into every language, even languages that
  don't exist yet.

What about pictures?

If you thought the story for books was mind blowing, wait until you think about
pictures. Books are easily quantifiable, but what about pictures? Well, consider
a computer monitor. It is made of small "picture elements", charmingly
abbreviated "pixels". A modern, high resolution monitor has over 2 million
pixels. Some have double or triple that. Each pixel is capable of being any one
of approximately 16 million colours. This is more than the human eye can
distinguish. Also, pixel size is getting reasonably close to point where, were
they smaller the human eye wouldn't be able to distinguish. A decade from now
monitors may well have reached the limit of our eye's perception.

Although we wouldn't have been able to say this back in the eighties when
computer monitors could only display rather poor, chunky, "pixelated" images
and in disappointingly few colours, we can now say that computer monitors, to
a reasonable approximation, can display anything the human eye is capable of
seeing.

Put simply, the entirety of human visual experience can be displayed on a
computer monitor. Everything you have seen up to this point, at every moment,
from every angle, at every time of day, is an image within the collection of
potential pictures that a computer monitor can display. So is everything you've
imagined, or could imagine. This includes, but is not limited to photos of you:
shaking hands with every celebrity (past and present),
standing on the moon, on a beach you've never been to, painting a new
masterpiece, receiving the Nobel prize, ballet dancing, meeting with the first
diplomatic delegation from an alien race, wearing the latest fashion five years
from now, at a party with a copy of yourself from every age you've been.
Anyone who has played with Photoshop knows about the existence of these photos
out there in the vastness of possibility.

Interestingly there are a lot more pictures we can see than books we can write.
This just adds weight to the common wisdom that a "picture paints a thousands words".
For each possible book there are over 10^11,622,844 photos!

In the realm of pictures it's even more true that it hasn't all been done
before.

A recipe to produce every possible picture

We can think of artists as discoverers of interesting
pictures within a vast state space of possible pictures. Naturally, artists
don't do it by searching through the vast possibilities. Such a search would
require no creativity. Nevertheless, it is possible, in priciple.

The recipe is very much like counting. We're all very familiar with how to
count. We start at 1 (or 0) and increment digits until we get to 9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Once we get to 9 we have run out of digits. What we do at this point is put a
1 in the "ten's house" and start at zero again.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

We continue to the process until we get to 99 and then we add a 1 in the
"hundred's house".

We do a similar thing for pictures. Each colour is represented by a number
between 0 and (approximately) 16 million. We start with the completely black
picture, made entirely of zeroes. We then increment the last pixel on the screen
which we'll choose by convention to be the one in the bottom-right corner. We
continue incrementing that colour until we get to (approximate) 16 million.
At this point we set it back to 0 and then increment the second last pixel to
1 and continue the process on the last pixel again.

This process is continued until every picture has been displayed on the
monitor. A computer program to do this task is quite short, on the order of
a only a few lines of code.

Even viewing every 10x10 black and white logo would take a long time

Now knowing how long it would take to read all possible books of 400 pages you
probably suspect that it's infeasible to sit in front of a computer screen
waiting for an interesting picture to eventually appear. This is true, but
perhaps this is only because we're selecting them from such a large space of
possible pictures. What if we looked at a much smaller space of possiblities?
Let's have a look at the space of all black and white pictures of 10x10 pixels.
The number of these is 2^100, which is a 31 digit number.

Now let's follow the recipe in the previous section and assume that we can view
one per second. Sadly, the age of the universe wouldn't even begin to be enough
time to see them all. The age of the universe is merely an 11 digit number. You
would need to multiple the age of the universe by 10^20 (a 20 digit number) to
have enough time.

The tragedy is that even if you did this even the most interesting pictures are
still pretty boring. There is only so much you can do with two colours. They
would look pretty awful by modern standards, even though they might have been
cutting edge in computer games of yore.

It really hasn't all been done before

I hope this little essay has convinced you that, at least for books and images,
there is a truly gargantuan space of possibility out there and that not even a
small part of it could be created by humanity no matter how much time we had or
how many of us there were. Your creativity is the method by which the good is
sorted from the bad, so get out there and start creating!