using Shannon's information to measure proof-of-work

johanatan

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Quote from: patvarilly on July 11, 2011, 02:46:10 AM

Quote from: casascius on July 09, 2011, 12:57:02 PM

Satoshi's algorithm is much better. If you switch away from weighting with the sum of difficulties, and go to the sum of log of difficulties, you introduce a new vulnerability into easily taking over the block chain. That's because someone could make a very long chain of "difficulty 1" blocks and they could quickly be made to weigh more than blocks being created at the current difficulty n, because they are n times more difficult to create, but only weigh log n, which is a much smaller proportion of n as n increases. All while difficulty 1 blocks will weigh the most in proportion to their actual creation difficulty. So this idea is a bunch of nonsense, merely adds unwarranted complication at the expense of security.

+1. This was pretty clear from the start of the thread. The rest of the thread has just devolved into metaphysical blah-blah nonsense about time, entropy, the universe and everything. Believe me, I do research in statistical mechanics for a living: I think of entropy long and hard every day. The full contents of this thread is a hodgepodge of big words patched together with duct-tape.

Surely then you can take a few of the more prominent claims of this thread and debunk [or critique] them then instead of asking us to 'just trust you' TM? Really, your post adds nothing to a scientific debate as it currently stands.

patvarilly

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Quote from: casascius on July 09, 2011, 12:57:02 PM

Satoshi's algorithm is much better. If you switch away from weighting with the sum of difficulties, and go to the sum of log of difficulties, you introduce a new vulnerability into easily taking over the block chain. That's because someone could make a very long chain of "difficulty 1" blocks and they could quickly be made to weigh more than blocks being created at the current difficulty n, because they are n times more difficult to create, but only weigh log n, which is a much smaller proportion of n as n increases. All while difficulty 1 blocks will weigh the most in proportion to their actual creation difficulty. So this idea is a bunch of nonsense, merely adds unwarranted complication at the expense of security.

+1. This was pretty clear from the start of the thread. The rest of the thread has just devolved into metaphysical blah-blah nonsense about time, entropy, the universe and everything. Believe me, I do research in statistical mechanics for a living: I think of entropy long and hard every day. The full contents of this thread is a hodgepodge of big words patched together with duct-tape.

Dusty

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Libertas a calumnia

I admit I'm not grasping your aim but I'm interested in knowing more.

Quote from: grondilu on July 10, 2011, 03:25:21 AM

Anyway, I just think my version is just more "pure", and that it can allow to get rid of the 6 block per hour limit, for instance.

For what I understand the 6 block limit x hour is not a limitation but a design choice, done to balance the number of blocks with the time needed to broadcast them over a global network: the more blocks per unit time, the higher the probability of chain splits and needed reorganizations.

grondilu

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Quote from: casascius on July 09, 2011, 12:57:02 PM

Satoshi's algorithm is much better. If you switch away from weighting with the sum of difficulties, and go to the sum of log of difficulties, you introduce a new vulnerability into easily taking over the block chain. That's because someone could make a very long chain of "difficulty 1" blocks and they could quickly be made to weigh more than blocks being created at the current difficulty n, because they are n times more difficult to create, but only weigh log n, which is a much smaller proportion of n as n increases. All while difficulty 1 blocks will weigh the most in proportion to their actual creation difficulty. So this idea is a bunch of nonsense, merely adds unwarranted complication at the expense of security.

Making a long chain of small difficulties requires time, as this information would be computed in a sequential manner. That is the whole point, actually. The other way of computing information is to make parallel calculus. This would require much more power. Shannon's information is easier to calculate by cutting it in smaller successive parts, i.e. in long chain of successive events, which is all what time is about.

I actually think there is no qualitative difference between my algorithm and Satoshi's, but I don't understand Satoshi's algorithm well enough. Anyway, I just think my version is just more "pure", and that it can allow to get rid of the 6 block per hour limit, for instance.

casascius

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The Casascius 1oz 10BTC Silver Round (w/ Gold B)

Satoshi's algorithm is much better. If you switch away from weighting with the sum of difficulties, and go to the sum of log of difficulties, you introduce a new vulnerability into easily taking over the block chain. That's because someone could make a very long chain of "difficulty 1" blocks and they could quickly be made to weigh more than blocks being created at the current difficulty n, because they are n times more difficult to create, but only weigh log n, which is a much smaller proportion of n as n increases. All while difficulty 1 blocks will weigh the most in proportion to their actual creation difficulty. So this idea is a bunch of nonsense, merely adds unwarranted complication at the expense of security.

hashman

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Quote from: grondilu on July 01, 2011, 04:37:52 PM

Guys, this stuff is totally blowing my mind. As I keep modifying my design again and again, I get to think more and more about the whole thing, and the more I do that, the more I realize how deep it is.

I think it goes way beyond currencies and information technology. I'm starting to get convinced that it is related to fundamental physical concepts such as time, energy, uncertainty principle and Everett's interpretation of quantum mechanics. I'm really starting to think that I'm up to something big.

The idea of using chained proofs of work to measure time was something that I immediately blew me up when I got to know about bitcoin. Now I realize why. This idea is full of profound consequences.

If one agrees to define time as "a causal sequence of events", then it does make sense to use probabilities of these events to measure time. And if you want to have additive properties for this thing you measure and that you call time, then it's not exactly probabilities you should use, but rather the Shannon information of these probabilities. Now, instead of saying you are measuring, what if you say that you are actually defining it?

Finally, if you remember that quantum mechanics is all based about probability waves, you're beginning to realize how cool this idea is.

I'm trying to figure out what you are doing here with your timestamp server, and how hashing changes entropy.
What time is it now?

vector76

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Sometimes when I'm feeling philosophical I think about this. If the entire future and past of the universe were laid out in a fourth dimension, why do we observe it only going one way? Most of the laws of physics work equally well with time reversed. The second law of thermodynamics does not. Entropy and time are clearly related, but what is the true nature of their relationship? Does entropy depend on time, or is it the other way around?

grondilu

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Quote from: vector76 on July 09, 2011, 05:34:14 AM

It is just as hard to find a hash with 30 leading zero bits as finding (approximately) a million hashes with 10 leading zero bits. The information content is the same, but they are not equally good for timestamping due to other considerations.

There are very deep implications behind this assertion. I'm still struggling to grasp them, but I believe this is the core idea behind using Shannon's information theory to measure time.

Quote

I think bitcoin is basically an eternity service combined with a
timestamping service. IMO it is somewhat poor at both, but it is a decent
starting point. I think considering the storage and timestamping sub-functions
separately is a move in the right direction.

I agree.

vector76

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I don't think this information theory thing is a bad idea, but at the core level I'm not really sure how it's different from the bitcoin system.

The only difference I see is that the bitcoin system uses a varying difficulty so that blocks are generated at a somewhat consistent rate even when the total information rate varies wildly. It is just as hard to find a hash with 30 leading zero bits as finding (approximately) a million hashes with 10 leading zero bits. The information content is the same, but they are not equally good for timestamping due to other considerations.

I think bitcoin is basically an eternity service combined with a timestamping service. IMO it is somewhat poor at both, but it is a decent starting point. I think considering the storage and timestamping sub-functions separately is a move in the right direction.

grondilu

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Quote from: bji on July 08, 2011, 05:59:19 PM

It feels like you're trying to create an algorithm for computing proof-of-work that adheres to some rules other than the fairly straightforward proof-of-work rules that Bitcoin uses. What exactly is the benefit of using "Shannon Information Value" as a metric for sufficiency of the proof-of-work, versus a simple empirical-difficulty approach that Bitcoin uses?

Amongst my objectives:

- separating the distributed timestamping server from the rest of the bitcoin application. I believe a timestamping server should be an application by itself, as it could be used by other distributed systems ;

- getting rid of the 6 blocks per hour limit ;

- finding a theoretically ideal model for the idea of measuring time using chained proofs-of-work ;

- implementing bitcoin (or a bitcoin alike system) in a higher level language than C++ ;

Quote

Also, am I reading it correctly - is the data itself included in the hash calculation?

Yes, but only if the user wants it to. He can really put anything he wants, including a hash.

Quote

If that's so then it is significantly more expensive to compute hashes than with this than with Bitcoin, that always hashes an 80 byte header regardless of the payload size. Because of this, 'miners' in your system are incented to include the smallest payload possible because the hashes can be computed faster for them leading to a greater chance of 'beating' other miners to a successful hash. With bitcoin, there is a greater cost to larger payloads in blocks in that the cost of verifying the transactions is greater; but the cost of verifying transactions pales in comparison to the hash computation work, and so miners can include a reasonable number of transactions without worrying about a negative impact on hash computation time. If you include the payload in the hash calculation, then you're making the cost of computing hashes more expensive for larger payloads which, as I said, will encourage miners to include the smallest payload possible, and I don't think that's healthy for a distributed work system.

It will indeed encourage users (and not miners, which are different people), to use the smallest possible payload. I see this as a healthy way of saving memory space in the database. Basically instead of puttting Justin Bieber's last concert video in the database, Justin Bieber's fans will instead put the hash of the video. It will fullfill the purpose of timestamping the data.

It aims to be a timestamping server, not a data storage system.

bji

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Can you explain what you are trying to achieve? I read the code and I don't really understand the point of it. Here are the comments that give a brief description of the purpose:

Code:

################################################################################
#
# This code is inspired from Satoshi Nakamoto's bitcoin (see bitcoin.org).
# This is quite a different project, though.
#
# All timestamps should be of the following format:
# 
# PREVIOUS_INFORMATION_VALUE NONCE PAYLOAD_DATA
#
# where:
#
# - PREVIOUS_INFORMATION_VALUE is a positive floating number.  It has to have
# many decimals, as it should include the proof of work.
#
# - NONCE is a positive integer in decimal.  Its logarithm must not exceed the
# Shannon information value of the timestmp.
#
# - PAYLOAD_DATA is some data
#
# For each timestamp, the new information value is calculated by adding the
# previous information value and the Shannon information value of the
# timestamp.
#
# In a nutshell, for a string whose sha256 is h, the shannon information value
# is:
#
# ln (2 ^ 256 / h)
#
# It is basically the opposite of the logarithm of the probability for this
# sha256 to be as low as h.
#
# Sizes of payloads are cumulated and new payloads are accepted as long as the
# total size doesn't exceed the total Shannon information of the chain.

It feels like you're trying to create an algorithm for computing proof-of-work that adheres to some rules other than the fairly straightforward proof-of-work rules that Bitcoin uses. What exactly is the benefit of using "Shannon Information Value" as a metric for sufficiency of the proof-of-work, versus a simple empirical-difficulty approach that Bitcoin uses?

Also, am I reading it correctly - is the data itself included in the hash calculation? If that's so then it is significantly more expensive to compute hashes than with this than with Bitcoin, that always hashes an 80 byte header regardless of the payload size. Because of this, 'miners' in your system are incented to include the smallest payload possible because the hashes can be computed faster for them leading to a greater chance of 'beating' other miners to a successful hash. With bitcoin, there is a greater cost to larger payloads in blocks in that the cost of verifying the transactions is greater; but the cost of verifying transactions pales in comparison to the hash computation work, and so miners can include a reasonable number of transactions without worrying about a negative impact on hash computation time. If you include the payload in the hash calculation, then you're making the cost of computing hashes more expensive for larger payloads which, as I said, will encourage miners to include the smallest payload possible, and I don't think that's healthy for a distributed work system.

grondilu

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I'm back on coding, as I am finally happy (more or less) with my networking design. I won't use IRC or other fancy stuffs finally (I even considered using twitter via twidge). Instead, I will use a IRC-inspired network. All nodes will have a full copy of the database, but only those with public IP and CGI-capable webserver will be able to offer synchronization service to other nodes. With enough servers and enough connectivity, the whole network can be decentralized and uniform.

I also came up with quite a deep idea: balancing Shannon information with memory size. It's quite difficult to explain and I don't yet have a clear explanation of why it should be done, but I'm pretty sure it should be done.

I have already implemented this idea for the payload (this is obvious), for the nonce (it's a bit less obvious) and recently I understood I should do it for the timestamp itself (this is not obvious at all, but it might be the most important idea).

Here is my code so far (the timestamp balancing is not implemented yet):

$ xz < timestamp.sh | base64
/Td6WFoAAATm1rRGAgAhARYAAAB0L+Wj4CtIDzJdABGIQkY99Bhqpmevep9vaWgy9uJUdLDJuwGD
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grondilu

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Merit: 1076

I'm afraid I must confess I am losing motivation on this project, as I struggle to have nodes communicate and synchronize.

It would be *so* much more simple if everyone had a public IP, but we still live in a IPv4 world, so I would have to deal with NAT traversal and stuffs like that. Using IRC could be a solution but I don't want to spam a irc network.

I publish the current state of my code, though:

$ xz < timestamp.sh |base64
/Td6WFoAAATm1rRGAgAhARYAAAB0L+Wj4CdwDrhdABGIQkY99Bhqpmevep9vaWgy9uJUdLDJuwGD
AzBbm+1fOW26eoYFsF8Nm/I035vPvarX8iWIe9TEJiuDC2RFK5nutHK8tfFHyB7Vatw5Duk/Pdbs
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lrHEZ/sCAAAAAARZWg==

markm

legendary

Activity: 2940

Merit: 1090

A lot of quantum mechanics purported spookiness rests upon Bell's Theorem.

So before getting too carried away about what quantum stuff can do, it is probably worth checking out

http://front.math.ucdavis.edu/search?a=Joy+Christian&t=bell&q=&c=&n=25&s=Listings

-MarkM-

grondilu

legendary

Activity: 1288

Merit: 1076

Guys, this stuff is totally blowing my mind. As I keep modifying my design again and again, I get to think more and more about the whole thing, and the more I do that, the more I realize how deep it is.

I think it goes way beyond currencies and information technology. I'm starting to get convinced that it is related to fundamental physical concepts such as time, energy, uncertainty principle and Everett's interpretation of quantum mechanics. I'm really starting to think that I'm up to something big.

The idea of using chained proofs of work to measure time was something that I immediately blew me up when I got to know about bitcoin. Now I realize why. This idea is full of profound consequences.

If one agrees to define time as "a causal sequence of events", then it does make sense to use probabilities of these events to measure time. And if you want to have additive properties for this thing you measure and that you call time, then it's not exactly probabilities you should use, but rather the Shannon information of these probabilities. Now, instead of saying you are measuring, what if you say that you are actually defining it?

Finally, if you remember that quantum mechanics is all based about probability waves, you're beginning to realize how cool this idea is.

grondilu

legendary

Activity: 1288

Merit: 1076

Quote from: Jaagu on June 30, 2011, 10:07:53 AM

I'm burning with curiosity: did you just devise a new form of freecoin or you're just suggesting a major upgrade to the existing bitcoin protocol?

Didn't know about this freecoin thing. I'll have look someday if I have time.

I had several other ideas, such as using the chain as a data storage, and having nodes pay for each bit of information they store in the chain.

Also, I'll use general bitcoin addresses (with any version number from 0x00 to 0xFF).

Here is the current state of my code (it doesn't work yet but it will give you an idea of where I am):

$ xz < timestamp.sh | base64
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ref/ZUvM0sxve908bq0+m0yTjagv+CesmkSFc939NxSNx4zXFnDuSFA4cwy0L/qcFfhHoiUQGe8l
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Jaagu

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Quote from: grondilu on June 28, 2011, 07:22:21 AM

... I realised that the cryptographic timestamp server I have implemented could be used as a currency. I'll describe how later. Anyway this would turn information, or time, into a currency.
Crazy stuff, really.

I'm burning with curiosity: did you just devise a new form of freecoin or you're just suggesting a major upgrade to the existing bitcoin protocol?

johanatan

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From this:
http://www.noanswersingenesis.org.au/dawkinschallenge.htm

one can see (in the 3rd and 4th paragraphs of the 'Information' section) that it is the *number of possibilities* (not precisely 'uncertainty') which is halved by the transmission of a single bit. In your examples, the two possibilities are:

1 - it has rained X number of continuous days in Y
2 - it has not rained X number of continuous days in Y

If instead we had an example where there were 8 possible outcomes, as each additional bit comes in, the number of remaining possibilities is reduced by 1/2. 8 > 4 > 2 > 1. After receiving 3 bits, we have precisely identified which of the 8 possibilities occurred.

markm

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It is not really one bit, it is one additional bit.

It was conceptually easy to transpose halving uncertainty into doubling certainty, but trying to then re-write the sensible-sounding story of how your certainty doubled as somehow being a case of your uncertainty having halved was beyond me. It'd seem to imply you were 100% uncertain until the card was flashed then became 50% uncertain, which doesn't sound right at all. So the whole idea that halving uncertainty implies doubling certainty seems dubious. Boolean logic might work better somehow maybe as it smells of one of those "from x implies y we cannot deduce that y implies x" type logic thingies.

Sounded good for a moment though, didn't it? Wink

We were 50% uncertain that it was the one it turned out later not to be, until the card was flashed, then we were 100% uncertain it was the one it turned out not to be... Oops, uncertainty doubled, not halved.

-MarkM-

becoin

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Quote from: markm on June 29, 2011, 09:57:18 AM

Okay, how about re-phrasing it by saying that the prior certainty is doubled?

Before the nurse flashed the card, you were 50% certain it was whichever it turned out later to be.

After the nurse flashed the card, you were 2 * 50 = 100 % certain it was whichever it turned out to be.

-MarkM-

As a logical block above is okay, but then the entire article should be rewritten as some assumptions won't be correct. You can't double the value of something by multiplying with 1, because 1 bit is, by definition, 1 binary digit - '1' or '0'. Unless, you can prove that 1 bit = 2. But then, what is 2?

Topic: using Shannon's information to measure proof-of-work (Read 3798 times)