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πFS

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Re: πFS

#131

Post by pocksuppet »

School-Cotton wrote: post #128
windward wrote: post #96

>One of the properties that π is conjectured to have is that it is normal conjectured Glad to see one of my pet points of pedantry come up. No non-constructed irrational number has never been proven to be normal or disjunctive.

What do you mean by "non-constructed" here?

You can design a number. Just take all finite digit strings in order of length and numerical order: 0.123456789 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 ... 99 000 001 002 ... 999 0000 0001 ...

obviously it contains every finite digit string in base 10. I can't prove the digits are uniformly distributed in every base - you'd have to be more clever but you see the idea.

Re: πFS

#132

Post by hatthew »

ithkuil wrote: post #124
hatthew wrote: post #110

Earlier quoted context omitted.

TFA addresses this > 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.

Why stop at bytes? Let's split it in individual bits and then look up the bits in pi! But Pi's binary expansion is not very practical for this purpose, since it's 11.0010... OTOH. e is 10.1011... Let's stick to fractional digits (the ones right of the binary point) at index 0 we have 1 and at index 1 we have 0. So, to encode a stream of bytes so that each bit is encoded as the index of that bit in the e, all you need…

genius

Re: πFS

#133

Post by whynotmaybe »

ChrisMarshallNY wrote: post #63
Levitating wrote: post #58

Earlier quoted context omitted.

Even then I don't see a direct way to extract a list like this.

I think it's safe to assume that dang has access to tools that we mortals are unable to comprehend, without being driven to madness.

I can only imagine opening dbeaver and running "select * from hn.posts where site like '%github.com/philipl`"

Re: πFS

#135

Post by gowld »

liamYC wrote: post #99
adzm wrote: post #12

It is worth noting that as the length of data increases it becomes extremely unlikely that the index and length of the sequence within pi would actually be smaller than the data.

Point taken about the index potentially being really long. Why would the length be longer than the data? Don’t you need to find the right sequence?

For a given length of data, considering all possible data of that length, it's impossible for the median length to be shorter than the data length. There aren't enough strings of that length that early in the data.

Re: πFS

#136

Post by nvader »

ithkuil wrote: post #124
hatthew wrote: post #110

Earlier quoted context omitted.

TFA addresses this > 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.

Why stop at bytes? Let's split it in individual bits and then look up the bits in pi! But Pi's binary expansion is not very practical for this purpose, since it's 11.0010... OTOH. e is 10.1011... Let's stick to fractional digits (the ones right of the binary point) at index 0 we have 1 and at index 1 we have 0. So, to encode a stream of bytes so that each bit is encoded as the index of that bit in the e, all you need…

Hang on hang on let me write a CUDA kernel for this. This is going to be really huge.

Re: πFS

#137

Post by gowld »

ndiddy wrote: post #106
MisterTea wrote: post #8

Reminds me of: https://www.spronck.net/sloot.html Further reading: https://en.wikipedia.org/wiki/Sloot_Digital_Coding_System

I looked into this a bit a while ago, what Sloot did was at least a little novel. Basically the way his encoding scheme actually worked was that it would store each line of video into a database, encode each video frame as a series of line lookups, and then store that encoded frame into another database. Then each video is a series of frame lookups. When you hear accounts of him being able to demo smooth playback of…

Block deduplication. This is how Enterprise storage arrays (such as NetApp Deduplication) and local file systems (like ZFS and Microsoft ReFS via Windows Server Data Deduplication) (and normalized databased in general) work.

Re: πFS

#138

Post by School-Cotton »

pocksuppet wrote: post #131
School-Cotton wrote: post #128

Earlier quoted context omitted.

What do you mean by "non-constructed" here?

You can design a number. Just take all finite digit strings in order of length and numerical order: 0.123456789 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 ... 99 000 001 002 ... 999 0000 0001 ... obviously it contains every finite digit string in base 10. I can't prove the digits are uniformly distributed in every base - you'd have to be more clever but you see the idea.

But pi is also "constructed", in the sense that you can write down a constructive definition for it, for example \sqrt{6 \times \sum_{k=1}^\infty \frac{1}{k^2}}.

So I suppose maybe OP meant we haven't proven any number to be normal (or not) that is not designed to be normal (or not) ?

Re: πFS

#139

Post by gowld »

smaudet wrote: post #122
mike_hock wrote: post #16

Earlier quoted context omitted.

So does every other random infinite sequence of bits. The unintuitive part comes from infinity, not pi. It also doesn't contain all past and future knowledge because it also contains all possible falsehoods about the past and future in a way that's indiscernible from the truth. Encoding information as an offset into a pseudorandom sequence is no more storage efficient than storing the information directly.

Keyword is conjectured. Infinities of random sequences exist that can be shown not to contain all data, 0-8 (base 10) is one such random sequence that is trivially proven to never contain 9... There are no known patterns to pi, but, (I am legitimately curious about this), are there any known sequences e.g. of 1 million 0s and a single other digit within the decimal sequence of pi? Given how it (pi) looks, I'm of the…

The longest consecutive sequence of decimals digits found in pi is a sequence of 13 8s. All other digits have a sequence of length 12.

https://bellard.org/pi/pi2700e9/pidigits.html

Re: πFS

#140

Post by gowld »

anthonj wrote: post #40
bobim wrote: post #6

This is disturbing to realize that pi then contains all the past and future knowledge, including when I'll pass away.

So does a random number generator

You need to be more specific in order to make that statement falsifiable.
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