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File system that stores location of file in Pi

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Re: File system that stores location of file in Pi

#61

Post by damon_c »

erikb wrote: post #57
nadam wrote: post #56

When I was young I had this idea that any hard drive can be compressed into 100 bytes. The compressed data is a 4 dimensional vector, a component of the vector is a 25 byte floating point number, and represent the space-time coordinates of the hard drive. (For example my hard drive in 1994 marc 3 23:00:45.456 at a specific place in Budapest) The extractor algorithm just have to simulate the universe from the big bang…

Well, let's assume that the past is constantly changing. The path leading from the start to the universe to the writing of your 4D vector would also change and therefore your vector itself might change automatically with every change to space-time. Or would that still be called deterministic?

Good point. It might be best to use a 5D vector to account for this.

Re: File system that stores location of file in Pi

#62

Post by baddox »

nadam wrote: post #56

When I was young I had this idea that any hard drive can be compressed into 100 bytes. The compressed data is a 4 dimensional vector, a component of the vector is a 25 byte floating point number, and represent the space-time coordinates of the hard drive. (For example my hard drive in 1994 marc 3 23:00:45.456 at a specific place in Budapest) The extractor algorithm just have to simulate the universe from the big bang…

Even if all your assumptions hold, of course, you can still only represent 2^800 universes, and thus only 2^800 different file systems. That's probably sufficient for cases with infrequent read-write cycles, assuming that your floats tend to cover useful time-space coordinates (i.e. where and when a hard drive could plausibly reside). I'm not sure how "space-time coordinates" would work (where is the origin and what is the granularity?), so I don't know if it's likely.

That being said, I would be more concerned by the philosophical and practical consequences of such capability, namely the ability to read hard drives in normally inaccessible locations and hard drives in the future.

Re: File system that stores location of file in Pi

#63

Post by mrpopo »

Tuna-Fish wrote: post #42
microcolonel wrote: post #31

Earlier quoted context omitted.

You laugh now, but when we develop a trivial method to calculate pi and other irrational constants to quadrillions of digits, this will be wonderful.

By the pigeonhole principle, no matter how fast you can calculate pi, you cannot actually use this to compress data. The index to relevant sequence is on average >= the size of the data to be stored.

I was thinking so hard trying to give myself a clear explanation of why this type of compression was impossible! Thank you.

Here is the pigeonhole principle on wikipedia:

http://en.wikipedia.org/wiki/Pigeonhole_principle

Re: File system that stores location of file in Pi

#64

Post by nsajko »

erikb wrote: post #57
nadam wrote: post #56

When I was young I had this idea that any hard drive can be compressed into 100 bytes. The compressed data is a 4 dimensional vector, a component of the vector is a 25 byte floating point number, and represent the space-time coordinates of the hard drive. (For example my hard drive in 1994 marc 3 23:00:45.456 at a specific place in Budapest) The extractor algorithm just have to simulate the universe from the big bang…

Well, let's assume that the past is constantly changing. The path leading from the start to the universe to the writing of your 4D vector would also change and therefore your vector itself might change automatically with every change to space-time. Or would that still be called deterministic?

Could yóu explain how/why do you think the past is constantly changing?

Re: File system that stores location of file in Pi

#67

Post by nadam »

baddox wrote: post #62
nadam wrote: post #56

When I was young I had this idea that any hard drive can be compressed into 100 bytes. The compressed data is a 4 dimensional vector, a component of the vector is a 25 byte floating point number, and represent the space-time coordinates of the hard drive. (For example my hard drive in 1994 marc 3 23:00:45.456 at a specific place in Budapest) The extractor algorithm just have to simulate the universe from the big bang…

Even if all your assumptions hold, of course, you can still only represent 2^800 universes, and thus only 2^800 different file systems. That's probably sufficient for cases with infrequent read-write cycles, assuming that your floats tend to cover useful time-space coordinates (i.e. where and when a hard drive could plausibly reside). I'm not sure how "space-time coordinates" would work (where is the origin and what…

" That's probably sufficient for cases with infrequent read-write cycles, assuming that your floats tend to cover useful time-space coordinates (i.e. where and when a hard drive could plausibly reside). I'm not sure how "space-time coordinates" would work (where is the origin and what is the granularity?), so I don't know if it's likely."

Now I have calculated a little:

The age of the universe is 8 * 10^60 in planck time units:

http://www.wolframalpha.com/input/?i=universe+age+%2F+planck...

So if the simulation is for example something like a cellural automaton with a planck-time (5.4 * 10^(-44) sec) step-size, than assuming we use fix-point numbers, 26 bytes suffice. (25 bytes are just not enough, 256^25 = 1.6 * 10^60)

Suprisingly the size of the universe is 5.4 * 10^61 in planck-length units:

http://www.wolframalpha.com/input/?i=planck+length+universe+...

So again, we need 26 bytes, for a super fine representation. I was one byte off for all components, so we need altogether 104 bytes.

Re: File system that stores location of file in Pi

#68

Post by TheAuditor »

I had played with this idea some time back and gave up after some very specific flaws came became clear.

The good probability that a 5 digit combination is found in Pi will be in the range of locations above 10000, for example I once located by 6 digit phone number in position 685214 which was not actually helpful at all.

Further we are not sure if Pi is normal hence the better idea would be use a simple computable normal series.

It was just yesterday I uploaded a paper that presents a idea for Compressing Random Data to -> https://www.academia.edu/7620004/Advanced_Compression_Techni... which proposes an Idea to push multiple bytes represented by a positions in a computable number series into small representation and generate them on the go when required. (need lot of improvement to actually apply)

Re: File system that stores location of file in Pi

#69

Post by irodov »

zaroth wrote: post #5

Now, we all know that it can take a while to find a long sequence of digits in π, so for practical reasons, we should break the files up into smaller chunks that can be more readily found. In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π. Definitely worth a chuckle. Very cute idea and implementation.

Could have made it even better by considering individual bits separately, and using their positions.

Re: File system that stores location of file in Pi

#70

Post by TheAuditor »

Tuna-Fish wrote: post #42
microcolonel wrote: post #31

Earlier quoted context omitted.

You laugh now, but when we develop a trivial method to calculate pi and other irrational constants to quadrillions of digits, this will be wonderful.

By the pigeonhole principle, no matter how fast you can calculate pi, you cannot actually use this to compress data. The index to relevant sequence is on average >= the size of the data to be stored.

I know :D I tried it for past 6 months and then gave up on it 2 months back, for the same reason. how ever that search gave rise to a better idea to compress files. Not yet usable but don't have all these issues with it. If you are interested you can read it at https://www.academia.edu/7620004/Advanced_Compression_Techni... It is based on data being represented as a position and not as the values in a computable number series .
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