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Title: using Shannon's information to measure proof-of-work Post by: grondilu on June 25, 2011, 08:31:31 PM Guys, I am so excited about this new idea of mine that I can't wait until tomorrow when I get my usal internet access to tell it to you. So I'm writing this from a cybercafé. I hope you'll enjoy.
I was working on my catalaxia project and I was thinking very hard about how I could avoid using Satoshi's compicated algorith for adjusting difficulty. Somehow I beleived there should be a more elegant, mathematically pure way to do this. I was troubled by the idea of mesuring the "strengh" of a block chain, and I must confess I never managed to understand exactly how Satoshi does it. I wanted something much more simple. Then I remembered my old lessons in physical statistics and information theory. Then I thought about entropy and Shannon's information concept. Basically shannon's information is a way to measure unlikelyness of an event. A bit like probability, but with additive properties. In probabilities, when two events e1 and e2 occurs in the same time, the probability of this to happen is the product of the probability: P(e1 & e2) = P(e1) * P(e2) Shannon wanted to have the same thing, but with additive property: I(e1 & e2) = I(e1) + I(e2) Obviously the solution was to use the logarithm function, so he came up with this formula: I(e) = - ln ( P(e) ) And he called that "the information". It's measured in bits if you divide by the natural logarithm of two, and it's quite a fascinating concept. Ok, enough for the theory. The idea now is to use this as a measure for the "weight" of a block. Basically all we have to do is to divide 2^256 by the block hash, and take the natural logarithm. The total information of the block chain is nothing but the sum of each information for each block. The good news is that we won't have to start the block chain from scratch or whatever, as the longuest block chain currently almost certainly has the highest Shannon's information. I think there are many advantages on this, such as simplicity and robustness. There are also many interesting implications such as the possibility to make the information being a inside secondary currency inside the block chain, which could be used to trade between miners in order to avoid chain forks. I'll explain later. There are many things to say about why I think this is a good idea, but right now I just wanted to tell it to you before someone else does, so I can claim the glory of being the first to have dropped it, in case it appears as great an idea as I think it is. Title: Re: using Shannon's information to measure block weights Post by: dinox on June 25, 2011, 10:21:05 PM I can assure you that satoshi's method is a lot simpler.
Title: Re: using Shannon's information to measure block weights Post by: Karmicads on June 26, 2011, 12:11:18 PM Then I remembered my old lessons in physical statistics and information theory. Then I thought about entropy and Shannon's information concept. That Del Shannon guy sure was an underrated hero wasn't he? Quote Basically shannon's information is a way to measure unlikelyness of an event. A bit like probability, but with additive properties. OH! That Shannon. Now we are talking heroes of another order of magnitude (no offence Del, wherever you are :D) Here he is: How many people realize that in 'coining' the term (pardon the pun) 'bitcoin' Satoshi was actually acknowledging (perhaps inadvertantly) the father of information theory? The 'bit' being the unit of information that halves prior uncertainty of an unknown value. It's generally recognized that Shannon essentially defined the 'bit' if he didn't literally coin the term (again, pardon the pun). I don't understand programming all that well nor mathematics either for that matter, but I do love information theory, so Shannon is a legend in my eyes, in that he devised the mens to quantify redundancy. I don't know how Satoshi's algorithm does the weight calculation, but I assume it's some sort of Bayesian approach, heavy on recursive looping too I expect. Quote In probabilities, when two events e1 and e2 occurs in the same time, the probability of this to happen is the product of the probability: P(e1 & e2) = P(e1) * P(e2) Shannon wanted to have the same thing, but with additive property: I(e1 & e2) = I(e1) + I(e2) Obviously the solution was to use the logarithm function, so he came up with this formula: I(e) = - ln ( P(e) ) And he called that "the information". It's measured in bits if you divide by the natural logarithm of two, and it's quite a fascinating concept. Fascinating indeed. Particularly for it's implications for entropy, but that's another story. BTW, even that explanation helped my mathematics understanding. I can see now, how the cumulative 'surprise value' of each bit, is derived from Shannon's Log function. Thanks for that. Quote The idea now is to use this as a measure for the "weight" of a block. Basically all we have to do is to divide 2^256 by the block hash, and take the natural logarithm. The total information of the block chain is nothing but the sum of each information for each block. I can't wait till you write a verbose non-mathematical description for us non-mathematical types. It sounds like a very grass roots 'bottom up' approach, to avoid the need to calculate the weight by measuring it directly. But again, I don't know how it's ordinarily done in Satoshi's implementation. Quote The good news is that we won't have to start the block chain from scratch or whatever, as the longuest block chain currently almost certainly has the highest Shannon's information. I think there are many advantages on this, such as simplicity and robustness. There are also many interesting implications such as the possibility to make the information being a inside secondary currency inside the block chain, which could be used to trade between miners in order to avoid chain forks. I'll explain later. I'll be looking forward to it. ;) Quote There are many things to say about why I think this is a good idea, but right now I just wanted to tell it to you before someone else does, so I can claim the glory of being the first to have dropped it, in case it appears as great an idea as I think it is. Well done ol' chap. I hope somebody will take note of this. It sounds like an elegant alternative. I don't suppose you ever read Richard Dawkins' article The Information Challenge (http://www.skeptics.com.au/publications/articles/the-information-challenge/), in which he honors Shannon and provides a great layman's explanation of information as an economic commodity and the relevance of redundancy. I particularly like the parallels it draws (in my mind at least), with energy and entropy. He comes tantalizingly close to venturing into this realm, but unfortunately forestalls it. Anyhow, I wish you well with this promising refinement and intuitively, I honestly do think you have a good development refinement to offer. Please, keep us informed. Title: Re: using Shannon's information to measure block weights Post by: Pieter Wuille on June 26, 2011, 12:36:00 PM Bitcoin counts blocks are 'worth' as much as the statically expected number of hashes that have been performed to generate it. As far as I can see, that's the theoretically best criterion possible.
Title: Re: using Shannon's information to measure block weights Post by: grondilu on June 27, 2011, 07:23:17 PM I worked hard during two days but I finaly wrote a minimalist distributed timestamp server in bash!!!
Unfortunately I am once again in a cybercafé now so I can't publish it right now. I'll do it tomorow, I promise. Stay tuned as I think this is gonna be an MAJOR BREAKTHROUGH in crypto anarchism! Title: Re: using Shannon's information to measure block weights Post by: bji on June 27, 2011, 07:55:55 PM I was working on my catalaxia project and I was thinking very hard about how I could avoid using Satoshi's compicated algorith for adjusting difficulty. Somehow I beleived there should be a more elegant, mathematically pure way to do this. I didn't read deeply enough to understand every aspect of Satoshi's algorithm, but I thought the basic idea was to average the block generation time for the previous two weeks and then compute a difficulty which, given the same expected computational power, would have resulted in the target 10 minute average interval. Basically, adjust the difficulty so that if it had been the difficulty over the prior two weeks, then everything else being equal, a block would have been produced on average once every 10 minutes. It seems pretty straightforward and "elegant" to me already ... Quote I was troubled by the idea of mesuring the "strengh" of a block chain, and I must confess I never managed to understand exactly how Satoshi does it. I wanted something much more simple. I don't understand why you think the block difficulty measures the "strength" of the block chain, or even what "strength" means in this context. Unless I am wrong (and I often am!), the only measure is how many blocks were produced over the past two weeks. Individual blocks are not considered. If it took 1 minute to generate 2015 blocks and then the next 1 block took 20159 minutes, there would be no adjustment to difficulty over the next two week period because exactly 2016 blocks had been generated in exactly 20160 minutes, which gives the perfect 10 minute average interval. The contents of the blocks and the actual time taken to produce the hash for any given block don't matter, so from the difficulty adjustment algorithm's point of view, all blocks are the same, the only metric is the average over 2016 blocks of the time taken to generate the hash. Quote The idea now is to use this as a measure for the "weight" of a block. Basically all we have to do is to divide 2^256 by the block hash, and take the natural logarithm. The total information of the block chain is nothing but the sum of each information for each block. The good news is that we won't have to start the block chain from scratch or whatever, as the longuest block chain currently almost certainly has the highest Shannon's information. What would you use this "weight" for? If it's for adjusting difficulty, I don't see how it's useful. Quote I think there are many advantages on this, such as simplicity and robustness. There are also many interesting implications such as the possibility to make the information being a inside secondary currency inside the block chain, which could be used to trade between miners in order to avoid chain forks. I'll explain later. Please do, as this paragraph confuses me utterly. Title: Re: using Shannon's information to measure block weights Post by: patvarilly on June 28, 2011, 08:08:59 AM From main.h, here's how a block's work gets calculated:
CBigNum GetBlockWork() const { CBigNum bnTarget; bnTarget.SetCompact(nBits); if (bnTarget <= 0) return 0; return (CBigNum(1)<<256) / (bnTarget+1); } The total work done up to a certain block is the sum of the work of all previous blocks, down to the genesis block Basically, the "work" the highest possible hash value divided by the maximum acceptable hash value at the block's difficulty. As Pieter Wuille remarked, this is just the expected number of hashes you'd have to calculate before solving a block. What you're suggesting calculating is -ln( 1 / "work" ) = ln( "work" ) and adding these up. Pieter is right to point out that the original definition of total work estimates how much computational power has been invested to date into securing the block chain. Your definition of total work would be appropriate only if it took a constant amount of calculation to get one an extra bit at the beginning of the hash to be zero. But it doesn't take a constant amount of work, it takes twice as much work. Here's a vivid example of what would go wrong. Say I have 16 block chained together, A1->...->A16, each of which has "work" of 2, and additionally, three blocks X->Y->Z, each of "work" 16. Under the original definition of aggregate work, the total work in A1->A16 is 32, while the total work in X->Z is 48. These two aggregate works are proportional to the amount of time it would take you to secure each block chain with a constant-speed miner. Under your definition of work, A1->A16 would have aggregate work 16*ln(2) = 11.1, while X->Y->Z would have aggregate work 8.3, even though X->Y->Z took much longer to secure. Title: Re: using Shannon's information to measure block weights Post by: grondilu on June 28, 2011, 11:11:16 AM From main.h, here's how a block's work gets calculated: CBigNum GetBlockWork() const { CBigNum bnTarget; bnTarget.SetCompact(nBits); if (bnTarget <= 0) return 0; return (CBigNum(1)<<256) / (bnTarget+1); } The total work done up to a certain block is the sum of the work of all previous blocks, down to the genesis block Basically, the "work" the highest possible hash value divided by the maximum acceptable hash value at the block's difficulty. As Pieter Wuille remarked, this is just the expected number of hashes you'd have to calculate before solving a block. What you're suggesting calculating is -ln( 1 / "work" ) = ln( "work" ) and adding these up. Pieter is right to point out that the original definition of total work estimates how much computational power has been invested to date into securing the block chain. Your definition of total work would be appropriate only if it took a constant amount of calculation to get one an extra bit at the beginning of the hash to be zero. But it doesn't take a constant amount of work, it takes twice as much work. Here's a vivid example of what would go wrong. Say I have 16 block chained together, A1->...->A16, each of which has "work" of 2, and additionally, three blocks X->Y->Z, each of "work" 16. Under the original definition of aggregate work, the total work in A1->A16 is 32, while the total work in X->Z is 48. These two aggregate works are proportional to the amount of time it would take you to secure each block chain with a constant-speed miner. Under your definition of work, A1->A16 would have aggregate work 16*ln(2) = 11.1, while X->Y->Z would have aggregate work 8.3, even though X->Y->Z took much longer to secure. Thanks for your comment. I'll read that later but it's too late to discourage me, as I have just finished writing a prototype: http://s0.barwen.ch/~grondilu/cgi-bin/timestamp Title: Re: using Shannon's information to measure block weights Post by: grondilu on June 28, 2011, 11:22:21 AM Well done ol' chap. I hope somebody will take note of this. It sounds like an elegant alternative. I don't suppose you ever read Richard Dawkins' article The Information Challenge (http://www.skeptics.com.au/publications/articles/the-information-challenge/), in which he honors Shannon and provides a great layman's explanation of information as an economic commodity and the relevance of redundancy. I particularly like the parallels it draws (in my mind at least), with energy and entropy. He comes tantalizingly close to venturing into this realm, but unfortunately forestalls it. Anyhow, I wish you well with this promising refinement and intuitively, I honestly do think you have a good development refinement to offer. Please, keep us informed. Thanks for this reference. I am a huge fan of Richard Dawkins and I will read the link you provided. Your description of the subject makes it extremely relevant to this thread, as 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. PS. I'll put the code here as well, just in case: $ xz < timestamp |xxd -p fd377a585a000004e6d6b4460200210116000000742fe5a3e04f3f1c3b5d 00118842463df4186aa667af7a9fe191a5205b670958d0ded39d4a4e825c dfc1110b577a6d0b1e64741032ccd8aa98ace6d7eb38181b1318f591e6ea 5a1ab8468666c061e0478c4749a12e2c4db3ccabc3ae041f58fb29a5b4fd d74e5c2b81fca3676770810246e0bd2b2689cbfaef6451234ead354d983f 7ec9db6e65ceb2800a180c3674878c2400cf228bef78d69b8fa5bde53035 34e5756196704025897f202322783025df6b9e072f402fafa4450a19a000 b9acefc04c8747b155c14c8be1a1064f05dfb2d038ac1dd0260a8510079f 19334c3b2c2706f815d0fb4efb212b805450052bf0b620ed1a8fc0dd573b e50edce9d8ac91c6de527dedc7c36b9f86e21178557c92b2dab4825802f3 c02faa9005df9bb723e26af9f37d4fa158556407071719254d49d552ded1 7b145ccbac33064dff680ac7d6b796e5d0c6aee86b8af81343c95695f2fc bf5c62329e9dd46921c8688f8efc02a284355d10e63db8094902b934a2db aa7cce51053101a18c097db99ab39bcf23369a56d1ba8c667e38998515d6 8aca6965923965acee90c72c36b4124fc386bc5c625f564abd850795b838 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525b7b94d047bbb84f2bbba780e2e592a3aa1a38b5afd18671aefc87b993 54852946f74073b0d2b3496951c2ba9e2957002f90cf250c6580d3c40987 8252b648d4ec8f99c735759a2b2034b62bd9de89e4de41fe27933d380000 cc1997d0b2ba9a120001d738c09e0100b041e4c5b1c467fb020000000004 595a Title: Re: using Shannon's information to measure proof-of-work Post by: mcqueenorama on June 28, 2011, 03:12:20 PM Where's the distributed timestamp server in bash? I want to see that. And you should add it to the effort of the guys that are doing bitcoin cli tools:
http://forum.bitcoin.org/index.php?topic=2461.0 Title: Re: using Shannon's information to measure block weights Post by: becoin on June 29, 2011, 07:08:20 AM I don't suppose you ever read Richard Dawkins' article The Information Challenge (http://www.skeptics.com.au/publications/articles/the-information-challenge/), in which he honors Shannon and provides a great layman's explanation of information as an economic commodity and the relevance of redundancy. I don't understand this conclusion: Quote Shannon’s unit of information is the bit, short for “binary digit”. One bit is defined as the amount of information needed to halve the receiver’s prior uncertainty... Why is bit defined to remove only 50% of receiver's prior uncertainty? A bit should remove 100% of receiver's prior uncertainty! It is either '1' or '0'. There is no 1/2 binary digit?!“It rained in Oxford every day this week” or “It rained in the Sahara desert every day this week” - both remove 100% of receiver's prior uncertainty. What do I miss? Title: Re: using Shannon's information to measure block weights Post by: grondilu on June 29, 2011, 10:28:06 AM I don't suppose you ever read Richard Dawkins' article The Information Challenge (http://www.skeptics.com.au/publications/articles/the-information-challenge/), in which he honors Shannon and provides a great layman's explanation of information as an economic commodity and the relevance of redundancy. I don't understand this conclusion: Quote Shannon’s unit of information is the bit, short for “binary digit”. One bit is defined as the amount of information needed to halve the receiver’s prior uncertainty... Why is bit defined to remove only 50% of receiver's prior uncertainty? A bit should remove 100% of receiver's prior uncertainty! It is either '1' or '0'. There is no 1/2 binary digit?!In Shannon's meaning, one bit is an amount, it is not '1' or '0'. It is one bit. It halves the uncertainty because if you add one bit, you divide the probability by 2, by definition. Quote “It rained in Oxford every day this week” or “It rained in the Sahara desert every day this week” - both remove 100% of receiver's prior uncertainty. What do I miss? No, because the amount of information is not the same for both sentences, as rain in Sahara is much more of an unlikely event as rain in Oxford. Title: Re: using Shannon's information to measure block weights Post by: becoin on June 29, 2011, 12:23:41 PM Quote “It rained in Oxford every day this week” or “It rained in the Sahara desert every day this week” - both remove 100% of receiver's prior uncertainty. What do I miss? No, because the amount of information is not the same for both sentences, as rain in Sahara is much more of an unlikely event as rain in Oxford. Same confusion goes here: Quote He can’t see any details, so a nurse has agreed to hold up a pink card if it is a girl, blue for a boy. How much information is conveyed when, say, the nurse flourishes the pink card to the delighted father? The answer is one bit -- the prior uncertainty is halved. My answer is different. My answer is one bit -- the prior uncertainty is removed entirely, because pink card means girl. Unless, I don't understand what does 'flourish' mean in this context?Title: Re: using Shannon's information to measure proof-of-work Post by: markm on June 29, 2011, 01:57:18 PM 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- Title: Re: using Shannon's information to measure proof-of-work Post by: becoin on June 29, 2011, 03:03:01 PM Okay, how about re-phrasing it by saying that the prior certainty is doubled? 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? 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- Title: Re: using Shannon's information to measure proof-of-work Post by: markm on June 29, 2011, 04:14:52 PM 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? ;) 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- Title: Re: using Shannon's information to measure proof-of-work Post by: johanatan on June 29, 2011, 08:23:31 PM 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. Title: Re: using Shannon's information to measure block weights Post by: Jaagu on June 30, 2011, 02:07:53 PM ... 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 (http://www1.freshmeat.net/projects/freecoin) or you're just suggesting a major upgrade to the existing bitcoin protocol? Title: Re: using Shannon's information to measure block weights Post by: grondilu on July 01, 2011, 11:41:55 AM I'm burning with curiosity: did you just devise a new form of freecoin (http://www1.freshmeat.net/projects/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 /Td6WFoAAATm1rRGAgAhARYAAAB0L+Wj4EZuGttdABGIQkY99Bhqpmevep9vaWgy9uJUdLDJuwGD AzBbm+1fOW26eoYFsF8Nm/I035vPvarX8iWIe9TEJiuDC2RFK5nutHK8tfFHyB7Vatw5Duk/Pdbp pWtrgU7QPJ4r5SlLCm66N6dTMv+z9YjBRxe/aSYP3OvkaDOn1/20IfuE0tN6hsQAI5ZA1nOhrvc7 Kc1yszEZtcFnDbCTnSdh0J4L8YVx1CGwZPeOzMpTnnlgCyOOIjuQuVspHL/ullwun2zBkabJqeUT igMcl7WKK4HMlkUNd1bJtafvd+pL0xf1k8MssKFbPRqKewXsKPxOLBW3bCAiUY3TQlTtssocybPV 2meUxIq0OjNiX674DGNKd3rRk+XTRopGhIwAZ2dKfv4nvz/4uAkNpOW+nqyviq+CJQSS94pzJx8w 8OjAMi9j52GnRdcFvcrw9WMHinANzTO6CWNz3nI2W0kWCTw85Xdg+4lNynwwvcDG7Vewjli+M3xj zsVjPJ1I7JiKI6u/rOUBs+rRnzuDSY9d1jEWEj7tGDZxi5fmmD004FeFmh5tgjYCEeaP7xtrR3hE 0ydDZBoQk+Ynl3n7FBOuc4bFDBvFW0ezJUfARLZicuk2/UrvYppDSij3y6sSfnjODEOIriMOfM1c Gx/GRYz7VVkgQjhy6cpBZuCAa7VNt9hvgYrSaoCLNSXfHn6JNu1fAbL+0K4x69qereVoyx+aS7US FwnE1KWemWLP0daXeJOtgplI0cVFySX2Cp87atJIy0l1K31RllGJEC4VjDFa+Mqkj+pEpAGUs8rU 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bFBLKr2Ugmi4cO0tK2VDghuUIhJx9J3VdwviFMYdMdwHhXC9yLp4BM+kQFrqS4JtQ3hpJFF4ak2U YIM/y2gktArr7uvtDL+8E1+pPAoMmwwUtpJm4lETfe5llL6u4xjEVuYORbTJl2WWyEhM+WVqWsll /lDNWwz+N5WPHK/37vhu1uacrxO4cMtFgkORnTIBAq+H6ubUQ9OBHSpSa+M9p/wLquxc+5ZBcdNZ Gs/vMLL6DcjZxs1aEPGzYz4mrXFK/tF+miIjVhrYlu9Jyp91esS399MKIXWHW3b37pdjitXLqg55 Y/jcBX4UwZJ+Ah6DgegnYKd9UM9kShoqiMQpDvADBDqzrY3AVQyLGGUa6kKNV6iQkV+kCt8j1Hd8 zYX9G3etcDtvDxJEo1BgQOJBn7TVh+Mn5XGF3oOyZakkOGjjn/kTM0m636AfPcEGpyv7oe4x77s3 MNlrFySy4aYAAADK/hOZougkewAB9zXvjAEAQUgr3bHEZ/sCAAAAAARZWg== Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 01, 2011, 08:37:52 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. Title: Re: using Shannon's information to measure proof-of-work Post by: markm on July 02, 2011, 01:41:34 PM 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- Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 06, 2011, 11:57:04 AM 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 YX0MjiHGgjrcDRG11w16MT9B1woA+NBMyShdyZNGpS7b+6NSs1f7czZvdd/PvTl/i4vf/F6fIV9G yLBs4nvKeVKOTP2rcl8dIIb8me/ruGrFCMMQxekJIZEI0KLY1BzsMWfh4NLUnycRDo2p93vPK72a MrVObv060LgzOPLbBGhSoLu3SuAXDLnZrKGGWuob16IYTGjfRSDylKJei4ZOi5e6bXZCVhdCSLPe WGU25gQr2CkIwM6TMBFEsxkqjYRD3n2AYYr7/hljwrMDDe4a9aRJkCm85uEoznx2+rQb7OM9VMER z2yAONaVu3gRxWdGT43xLDIhAyUDlc07S7MiWmRZd++Tn9eaJZ+Bii8eSzXU8C93lGR1nz5Qc2ju E5x9cxUwhu5d1w2n+5u9YzMM7lHZl2UYSwKEtyuFTZi8x0M+AHi5WvJBQKz9Q5vb15u0JVE/VEM2 ofiGKkTEFJT2spwLzwDaGKrG3NR35r+LYxD86v6TcrGwq7F0qsHU0W7XkXdwPfo7gso+0TrBg/Bj ZB7ezOnioE+A7J/NZPfOqJEUIyZpSV1bqT+pSQJBN4I9ACr93PgGyxlHvo0K1y+JVop3lUBSMKzu UAI4CRt5Lao3opCFSQaIh6WTiszJx7d9A0y7Qgn1BfZmNnR52DTgjFwa852RtHlS5SsLvoD35u43 u651KHbvnK5IwjnHEB+kKU9U8q1W4HYYAsyc7JeDzlboUMvXkWHQubUPq7V0rm0wC+9aK80ybX/b 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S5WzhsVHul8AuvyTJOkik/D9goPynRaw/twnuxXKfbnr/E8VR4lUy9KORxK7HNceLyrMhrrqABJo sV3+ND6qh0mUu3DXjLKABHYoytxPLGepkyrYUfWAMVVT1XnuV3G5CGy3IiJVwDxM6iFQjeOlRdkb DA/ZPDAx0colQfEw9WHyCPNXmUa+fIzbZShJb5BaQhVM3JIu1Dgv8NmunV+umGXw5pqubZobSzNG 2HuCIJEv0Q3Vl68hqR8NadaPVwt/LYvGxlryOOLWCwvdLeEk803dMzkiwgJ1sPmYAmTpKZNv2sxu 2vrbeQVAYxq3EX/gapDqPx6xQ5faKzH7f9CVwqU/R3On4F1EASxCdNxAHj3phlH4hgaJiFxnIove A2+0+Bj6awW3PpshVUmUF9MI14mwfpfGIAJ5SfQCrrTeA9PIoa7MO+48IcdG4Zepaq3FDkqo3Lbj vIm2QTr4lgJRHMnltzHrBXaYXoEo+ixOvWyIpXNFmD3VplCsUbXMuNVCqCBwLfvXViJy7rUS9pMo uUAVqoTcvbziHciBGT/4sFRDZY37Wc96nJNExf/bTAO6dvqlFajP9fpQ8Gm974uIaBOCJwHs8fXH hBTgCbJdjd+GNnR9SWbwHiyyHslcP5mOwyKAjGAMBXbp8xiQ/9cqwdY7ZXT42QIrti5U4H9O1LtD YbfdXb42lUmvQR9Yis7r8COFxdLcAo7Jj68OTH5OYB3eH0/ciyRMingkvQDeOVmCn6oufFe4tdNx 5KmsjNQ4LPrHugOMGEJzuzlZD0+vX1R/WABWC1mde3/dpd8MMS6dj2qqmbkLD+UAmIVVRdpDszEP WFiwHC86RyNGJw3P27gghVoGpwc+nILT9XXt9H+yvUuXqAUibjeppNmn1bkZuOBIAF9BIz23NQEZ j93KOnnCcQo8Hygd7epPiOJ2TKiPXjo/uwwOLWeJFOt1//+OhumwMjZVQLM2vTeM/0VCPQV2Bb9S nWBWeGPPN67YMBWCdvyk0xoNV9uM+lBEB/Dj5mmbmyyZ7TPx1TZZ0ghjpRndGuFO+0EOKguXjfCl dIhmMxqhrhnHgtQ+vkOnlBPV1Nli89oA15ns+nGAItz/nFwR1EM2HIaossvMJLMiFmazENKMAdFZ 43VD+35qeYPo0u4yrWYTaAlEFXzacT0jiHWL+CZu1ZcGhd1ujwBulvZ/vZ//wgAB1B3xTgAA3whU lrHEZ/sCAAAAAARZWg== Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 08, 2011, 02:22:31 PM 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 AzBbm+1fOW26eoYFsF8Nm/I035vPvarX8iWIe9TEJiuDC2RFK5nutHK8tfFHyB7Vatw5Duk/Pdbs YX0MjiHGgjrcDRG11w16MT9B1woA+NBMyShdyZNGpS7b+6NSs1f7czZvdd/PvTl/i4vf/F6fIV9G yLBs4nvKeVKOTP2rcl8dIIb8me/ruGrFCMMQxekJIZEI0KLY1BzsMWfh4NLUnycRDo2p93vPK72a MrVObv060LgzOPLbBGhSoLu3SuAXDLnZrKGGWuob16IYTGjfRSDylKJei4ZOi5e6bXZCVhdCSLPe WGU25gQr2CkIwM6TMBFEsxkqjYRD3n2AYYr7/hljwrMDDe4a9aRJkCm85uEoznx2+rQb7OM9VMER z2yAONaVu3gRxWdGT43xLDIhAyUDlc07S7MiNToTPTRKIXY31j74Uf2uq3lJ1Ij/1sFg7yt8iPU+ ilJc/y58GcOb/NRkU225oDDdcl33Hwfjp8SmFXFtj2WA2J1em05TmnhQCjtPbWc2zLMiKAyYpVML 5AmiIMkQx5yqV7BKk6MR2qOKNKXoOsfeVYw1HuC88KATDBC3yTTyJqpXHK1Wevu2voQ10l5QVVSf 5kQArFceICvwIg/FVGr36nd6OSnL4v6/j+V1rENSwvzdf3cYYGj2948HyWyG62NZ2N9pOpUS2eds ib1tM0UApZnwlsrSm6/FjemihyRiEPecrPPkDsSOlHNeqkNzg1GD7LA+2UV4nSBARWOUzoDj5vja +0mncxoA/jodFVZq/JbZzoIvN32EmknQ22tI3JN9lF5xz4MuY/0zuoMfLthFV2nAXXd5fV9p03oa M7r1qi4vjpIPsfXTk8wLEw4+R2sDSrV/Msh7H55em8qkioCI2BYfIUn4uVr/60aiIZ75Ruq1qhIr M5kk/FsyAJTmoWZuxBdhoqXoow/IM/3UpenDUXDtUalvq1bqwaLzOK28NLgqIlM/MJfJ7Qj9i+KJ v6taJ/Oqh7jdks46s+Pmv4w+SNlecJbdoqaTTAoWD/fgxukv/qD9Bbp0MrxauZLLusyUj/lExJvb NLclqqzky1l2ToKAjsKUq5kuEGC4g9aeNjBm9qBE9F7nsmWa7egAHLGWLWmwMHjvBGQ8CDy9fU4E N8Ku/nL99utETrmbEy1xEWRr8ZCkUnG4utrG89REaCbZbo2psAiklgoWapaH/kY5y0TiV/IxJDbz rtohA4isjiwiwAxJGXLl9gP5bu67H72cHI3O9+bmVUpBm7S4KMGkBjvALKOwFQdntjWrtK6t1OhL igipw26rNPYoyY/Md/cp1aNnDeSPo4JyETwx58P/jV4xzdyghIBq9jiTqstPDopKMD7VbBsKphoj qEoiKbrvNxComA6GHgPlA68MPhSGvvuefdRAn8HdbVVHOcfmoOOUSzozqWXEzTYs4vhixPC3nukf yQByawYrNdo756ZfCEW2cZ0/P8ECiPEJm7j6cu3wT4dfT8kYkVnuEatSQo2pAkw24tl074pmD5kD vl2vXUdPBF4rbq4ivTs43BYW0HLET9G2mnw5Qq5KX1Gln/OoNs2L1NmjJXRnw87z1+oAYvTg3AR1 FwBKAZ2DOcnuE2wvIUl7IZonqq1+ShRdHVe8oFTzPr63rV3DQc5L2TH9egc1wfD6bWD/xS4LWWQf eElUyq3Dkn+pk1AxNwt2f22WLg4xctQbvCAUftWgU7w+6HvkOHl/VCOrxzl8jpjQ+p5IbrebG5gJ 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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: ################################################################################ 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. Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 09, 2011, 08:15:45 AM 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. Title: Re: using Shannon's information to measure proof-of-work Post by: vector76 on July 09, 2011, 09:34:14 AM 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. Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 09, 2011, 10:50:42 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. Title: Re: using Shannon's information to measure proof-of-work Post by: vector76 on July 09, 2011, 01:00:08 PM 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?
Title: Re: using Shannon's information to measure proof-of-work Post by: hashman on July 09, 2011, 04:38:17 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? Title: Re: using Shannon's information to measure proof-of-work Post by: casascius on July 09, 2011, 04:57:02 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.
Title: Re: using Shannon's information to measure proof-of-work Post by: grondilu on July 10, 2011, 07:25:21 AM 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. Title: Re: using Shannon's information to measure proof-of-work Post by: Dusty on July 11, 2011, 06:26:00 AM I admit I'm not grasping your aim but I'm interested in knowing more.
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.Title: Re: using Shannon's information to measure proof-of-work Post by: patvarilly on July 11, 2011, 06:46:10 AM 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. Title: Re: using Shannon's information to measure proof-of-work Post by: johanatan on July 11, 2011, 08:14:28 AM 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. |
