Library of "all" knowledge
Below you will read some thoughts from the field of absolutism and isolation from reality. The text will present philosophical and numerical inventions about a sub-complete and useless library of everything and everything. More precisely, the images of everything and everything. If you are not afraid, then I ask for an article. As calculations showed, the Earth will have to be disassembled. And not one.
These thoughts were inspired by the post of the Program as a work of art , which told about a book in which there was a quote: “sooner or later, any civilization will come up with both the Pythagorean theorem and the atomic reactor. But will she draw the same pictures, will she write the same music and make the same films? Surely not. ” And if this is not so?
That's what I thought. All theorems, studies, paintings, photographs, books can be considered as subsets of some global set, which can be approximated due to the limited feelings and activities of the human brain to some limited and finite set (I know that many will disagree with this and may be right). In view of current technologies, such a multitude can be expressed as a picture of your monitor, because on it you can see the Pythagorean theorem, a diagram of an atomic reactor, paintings, films, etc. So the idea of a hypothetical library came up, which will contain “all” information that humanity can to know. And we will do this by creating a library of all (!) Drawings of a given size.
If we create an array of all such drawings, then in this library of drawings will be:
1. All kinds of photographs that have ever been taken or will be made, or all kinds of fragments of all panoramas.
2. All photos with your face, even those that were destroyed so that no one sees them. And there will be photos of you in all positions in all kinds of outfits that you can imagine.
2. All books of all authors, with any spelling of all kinds of fonts. Moreover, the pages will indicate where in the library and how to search for pages with continuations.
3. It will be painted in great detail who killed Kennedy and where Elvis flew. True, there will be stories about how Elvis was kidnapped by Vasya’s cherries in the garden with boomerang shovels at the ready.
4. All paintings that have been painted and which will be painted ever.
5. The frames of all the films that were shot and will be shot sometime. Moreover, there will be realistic shots of The Terminator, where Jim Carrey plays the main role.
6. Your entire biography.
7. Accurate data on the death of every ever living person in the world.
8. Description of all scientific discoveries of scientists.
9. All button accordions, jokes, jokes.
10. Description of this post and generally all posts on Habrahabr.
11. Photos of Mila Kunis in any fantasy.
12. Descriptions of all tracks, melodies and compositions with a detailed diagram of how to play these songs.
13. A lot of other fount of useful information about which we do not even guess, and perhaps never guess.
14. All possible images of all our thoughts that can be displayed on monitors.
and so on.
Let's proceed to the calculations.
We will simultaneously carry out calculations for two cases. Imagine a picture of size WHUXGA 7680 × 4800 px with a depth of 24 bits. A BMP drawing of this size will weigh somewhere around 105 MB:
P 1 = 2 log 2 105 × 2 23 = 2 29,714 bits.
To save money, let's consider a more standard option: 1366 × 768 px, 24 bits deep. A JPG file of this size with 80% quality will weigh somewhere around 1.32 MB:
P 2 = 2 log 2 1.32 × 2 23 = 2 23.401 bits.
Now let's calculate how many drawings of each type are possible. Each pixel is encoded with 24 bits, a total of 7680 × 4800 pixels, which means the picture contains (metadata does not need to be considered here):
N 1 = 24 × 7680 × 4800 = 884 736 000 bits.
For the second option:
N 2 = 24 × 1366 × 768 = 25 178 112 bits.
Then drawings of each type are possible:
M 1 = 2 884736000 pieces.
M 2 = 2 25178112 pieces.
So, for storage, the drawing of the first type will require:
I 1 = 2 884736000 × 2 29.714 / 2 43 = 2 884735986.71= 10 266332067.40 TB.
For the second,
I 2 = 2 25178112 × 2 23.401 / 2 43 = 2 25178092.40 = 10 7579361.04 TB is required .
That is, for the second case, we will have a number for the recording of which 7 579 361 characters are required, and for the first 266 332 067!
Further calculations will be a little more free. Take a three-terabyte screw (we will not consider RAID arrays, we will not consider loops, etc.). What I watched was, weight 0.63 kg or 10 -0.201kg Suppose that we can use any material on the earth to make a hard drive: water, metals, stones - everything goes into business. Then, when the earth mass m = 5,9736 × 10 24 kg we can make:
H = 5.9736 × 10 24 /10 -0.201 = 9,489 × 10 24 drives.
You can’t even imagine how much this is, but how much is small for our case.
How much land will we have to disassemble in order to build a base (this does not take into account all the infrastructure, peripherals and so on)?
For the first case:
The number of lands 1 = 10 266332067.40 / (9.489 × 10 24 ) ≈1.05 × 10 266 332 042 pieces.
Number of lands 2= 10 7579361.04 / (9.489 × 10 24 ) ≈1.05 × 10 7 579 336 pieces.
And, there is a suspicion that the whole Universe will not be enough for such a library ...
Of course, this library is only hypothetical, and even in theory it is absolutely useless, since with all the information listed above this library has no mechanisms search for the necessary information and for every useful information there will be a lot of options with misinformation.
Please pay attention to the fact that:
1. This library does not contain all the information that is in the world.
2. Yes, the concept of fragments is a wider, larger picture, in essence, it reduces in the limit to a library of one pixel from which any other image can be built. In my case, just the "pixels" are larger. In fact, for a "complete library" you need to consider images of all sizes, but to display what can be depicted so that our brain understands - these sizes, which are given in the calculations, are enough.
3. Yes, there are pictures of greater depth than 24 bits. But again, for the perception of information by our brain this depth is enough for us.
4. Yes, “War and Peace” will not fit on one sheet, but in the library there will be such files on which it will be written to which file and how to get to read the sequel.
5. Yes, in order for this to be a library of information, a reader and an output device are required.
6. Yes, there are other forms besides images in which works of art are formed: music, smells, etc. But they can be described as symbols or encoded.
7. Yes, this article does not bear practical significance.
Here is a library of all knowledge turned out.
PS Suddenly, somewhere in the wrong calculation. And then it turns out a bit too much.
The Update . Corrected the calculations, but the error did not affect the final output.