Topic: using Shannon's information to measure proof-of-work - page 2. (Read 3843 times)

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-

I'm not discussing the amount of information, but if a bit of information is removing 50% or 100% of receiver's uncertainty. If you've learned about the rain in Sahara that doesn't make you less uncertain about the rain in Oxford!

Same confusion goes here:

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?

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.
 

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.

I don't understand this conclusion:
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?

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

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
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595a

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

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.

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 ...


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.


What would you use this "weight" for?  If it's for adjusting difficulty, I don't see how it's useful.


Please do, as this paragraph confuses me utterly.

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!

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.

That Del Shannon guy sure was an underrated hero wasn't he?



OH! That Shannon. Now we are talking heroes of another order of magnitude (no offence Del, wherever you are  )  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.


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.
 

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. 


I'll be looking forward to it. 


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, 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.

I can assure you that satoshi's method is a lot simpler.

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.