[ANN][CLAM] CLAMs, Proof-Of-Chain, Proof-Of-Working-Stake, a.k.a. "Clamcoin"

[organofcorti]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

I'm certain A) is correct, but not so sure about B). Isn't the previous block already fixed in time?

[smooth]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

I'm certain A) is correct, but not so sure about B). Isn't the previous block already fixed in time?

It is absurd that a random point in time would not have equal expected time difference with the previous and next blocks. How could that possibly happen?  You could replay the blocks in reverse sequence, right?

[organofcorti]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

I'm certain A) is correct, but not so sure about B). Isn't the previous block already fixed in time?

It is absurd that a random point in time would not have equal expected time difference with the previous and next blocks. How could that possibly happen?  You could replay the blocks in reverse sequence, right?

The time between poisson events is exponentially distributed and "memoryless". It's defined nicely here: https://en.wikipedia.org/wiki/Exponential_distribution#Memorylessness. Since the process is memoryless the forward or reversed sequence of inter-block durations are just as likely as any other arbitrary sequence of the same inter-block durations.

I could well be making some kind of error of logic here, but:

* Pick any time random time, T.
* The expected time until the next block is always one minute.
* The time *since* the last block is always T - (time since last block).
* The time since last block is always known and is not always one minute.
* Therefore the expected time since the last block != the expected time until the next block.

[smooth]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

I'm certain A) is correct, but not so sure about B). Isn't the previous block already fixed in time?

It is absurd that a random point in time would not have equal expected time difference with the previous and next blocks. How could that possibly happen?  You could replay the blocks in reverse sequence, right?

The time between poisson events is exponentially distributed and "memoryless". It's defined nicely here: https://en.wikipedia.org/wiki/Exponential_distribution#Memorylessness. Since the process is memoryless the forward or reversed sequence of inter-block durations are just as likely as any other arbitrary sequence of the same inter-block durations.

I could well be making some kind of error of logic here, but:

* Pick any time random time, T.
* The expected time until the next block is always one minute.
* The time *since* the last block is always T - (time since last block).
* The time since last block is always known and is not always one minute.
* Therefore the expected time since the last block != the expected time until the next block.

Put all the blocks that have already happened on a line on a piece of paper, drawn to scale (scale = time). Now put another piece of paper on top and slowly slide the top paper to reveal the blocks. The expected time to reveal the next block is (always) one minute. If you stop at any random point and flip the paper over so the opposite set of points is hidden, and then start sliding in the opposite direction, the expected time to reveal a block at the moment when you flip the paper over is still one minute.

However, it is certainly true that like most logic "puzzles" the exact wording of the problem statement (and its interpretation if ambiguous) changes the answer.

EDIT: Interestingly, by the way, I think we had a very similar discussion a long time ago having to do with the Eligius payout method. My last sentence above likely applied to that discussion as well.

[TooDumbForBitcoin]

Typical organofcorti genius stuff

When organofcorti visits your thread, it's like having the Pope come to your bingo game.

Something I'm curious about, though:

Is it "organ of corti", or "organov corti"?

[dooglus]

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

   I don't believe that's a valid equation for the problem.

Why on earth not? If the last block was B seconds ago and the next block is in A seconds, then how far apart are the two blocks?

Isn't it A+B?

The above is the kind of math politicians use...  

If X is the time of the block picked.
A is the time of the next block
B is the time of the previous block

C is the average block time.

  Then
(1+( ( ((X+A) + (X-B)) /2) - X)) = C

should give you C as the average block time.  

What is "average block time"? Suppose blocks were found every minute, at the top of the minute, and my random point is 30 seconds past the minute. It's 30 seconds since the last block and 30 seconds to the next block. The time between blocks is 30+30.  ie. A+B=C

I did mean for A to be the expected time to the next block (ie. 1 minute), not the time of the next block (ie. Tuesday at 12:34 or whatever).

A, B, and C are all 60 seconds.

A) From a random point in time we all agree that the expected time to the next block is 60 seconds. I don't think anyone's going to argue with that (except that we find blocks a little too fast, so it's actually 59 seconds or something, but let's ignore that.

B) I don't think anyone can really make a reasonable argument that the same isn't true about the expected time to the previous block. Just record the block creation process happening and play it backwards. It's indistinguishable from playing it forwards. Like smooth's sliding paper revealing the blocks. You can slide in either direction and the expect time to the 'next' block (which is the 'previous' one when sliding backwards) is 60 seconds.

C) Can anyone argue that the expected time between blocks is not 60 seconds?

I put it to you that A, B, and C are ALL equal to 60 seconds, and that this isn't a contradition.

There is a rational explanation for this. I just like to make people figure it out for themselves

  -- dooglus the deceiver

[chilly2k]

What is "average block time"? Suppose blocks were found every minute, at the top of the minute, and my random point is 30 seconds past the minute. It's 30 seconds since the last block and 30 seconds to the next block. The time between blocks is 30+30.  ie. A+B=C

I did mean for A to be the expected time to the next block (ie. 1 minute), not the time of the next block (ie. Tuesday at 12:34 or whatever).

A, B, and C are all 60 seconds.

A) From a random point in time we all agree that the expected time to the next block is 60 seconds. I don't think anyone's going to argue with that (except that we find blocks a little too fast, so it's actually 59 seconds or something, but let's ignore that.

B) I don't think anyone can really make a reasonable argument that the same isn't true about the expected time to the previous block. Just record the block creation process happening and play it backwards. It's indistinguishable from playing it forwards. Like smooth's sliding paper revealing the blocks. You can slide in either direction and the expect time to the 'next' block (which is the 'previous' one when sliding backwards) is 60 seconds.

C) Can anyone argue that the expected time between blocks is not 60 seconds?

I put it to you that A, B, and C are ALL equal to 60 seconds, and that this isn't a contradition.

There is a rational explanation for this. I just like to make people figure it out for themselves

  -- dooglus the deceiver

   I guess I still don't get it.  If I just pick a random time, IE not when a block is found.  And not knowing when the last block was found, I can only estimate that the next block will be found in less then 60 seconds (based on a 1 minute block time average). And the same with the previous block less then 60 seconds assuming the time I choose is not exactly on a block found time. 
 
  Your example 30 + 30 = 60 (or 1 minute)  Makes sense.
  But 1+1 = 1 doesn't. 

I can almost see a) if nothing else is know and you select a time, then a block should be found within 1 minute.  But it's not a fact that, "If you select a random time the next block will be found in 1 minute".  If you change in to within, then I buy it.  Same for B. 

  I'm sure I'm just taking this to literal....         

[organofcorti]

Typical organofcorti genius stuff

Heh, probably not in this case.

When organofcorti visits your thread, it's like having the Pope come to your bingo game.

Something I'm curious about, though:

Is it "organ of corti", or "organov corti"?

Organ of Corti : https://en.wikipedia.org/wiki/Organ_of_Corti

[SebastianJu]

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

Are you sure that you used the same point in time to calculate the first 2 points? If C is correct then in average you should always find a point in or on a 1 minute timeframe. When judging a and b for the same point then this would mean the average has to be a fraction of a minute in each direction because when C is correct then the average for A and B can't be higher. I think that goes against probability.

Can you check if your script has no error really?

Edit: I see, you know the result? Then i guess i wait for where you deceived us.

[BayAreaCoins]

Then i guess i wait for where you deceived us.

Doog the Deceiver! 

[SebastianJu]

Then i guess i wait for where you deceived us.

Doog the Deceiver! 

He wrote it himself so i guess he used some wording to trick us with his theory.

Well, i can't find out. When i would chose a random point in the future then the next block after that point should be a half minute later, i think, too. At least when the blockchain reaches that point in time. So i can't figure it out.

[smooth]

As I said before, read the problem statement VERY carefully. The solution is there.

[TooDumbForBitcoin]

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

If t denotes the time a random CLAM block is generated, then

A) the average amount of time from that point t to the next CLAM block is 1 minute
B) the average amount of time from that point t to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Does this make Dooglus's "random point in time" equivalent to "the time a random CLAM block is generated"?

[smooth]

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

If t denotes the time a random CLAM block is generated, then

A) the average amount of time from that point t to the next CLAM block is 1 minute
B) the average amount of time from that point t to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Does this make Dooglus's "random point in time" equivalent to "the time a random CLAM block is generated"?

I don't understand what you are asking? Are you saying that a block is generated at the exact instant you pick? That is not the case in general.

[TooDumbForBitcoin]

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

If t denotes the time a random CLAM block is generated, then

A) the average amount of time from that point t to the next CLAM block is 1 minute
B) the average amount of time from that point t to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Does this make Dooglus's "random point in time" equivalent to "the time a random CLAM block is generated"?

I don't understand what you are asking? Are you saying that a block is generated at the exact instant you pick? That is not the case in general.

I'm saying that t denotes the time block xyz was generated as recorded by the blockchain.

 I repeatedly shout out different random historical block numbers, and write down the time t that the blockchain says each was generated.

A)  The average of "time from t to the next block" is one minute
B)  The average of "time from t to the previous block" is one minute
C)  The average time between CLAM blocks is also 1 minute

Dooglus is picking random points in time t.  I am picking random block numbers.

The set of three conditions A, B, and C, are equivalent for Dooglus's pick and my pick.

Does this equivalence make Dooglus's "random point in time" equivalent to "the time a random CLAM block is generated"?

It sounds like no, because my set of times contains x members, where x is the CLAM block height.  Dooglus's set of times has an unbounded quantity of members. 

[sgravina]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

The error is in your final assertion, "Wouldn't you expect ...".  No I wouldn't expect that.  First, statements A and B don't make sense.  The average amount of time from the chosen point in time is a singular number.  You probably mean the average of a distribution of randomly chosen points.  If you do mean that then A, B and C are all saying the same thing, because the occurrence of blocks is a poisson distributed random process.  The time a block is created is as good a chosen time as any.  Thus I would expect 1 minute = 1 minute = 1 minute.

[SebastianJu]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

The error is in your final assertion, "Wouldn't you expect ...".  No I wouldn't expect that.  First, statements A and B don't make sense.  The average amount of time from the chosen point in time is a singular number.  You probably mean the average of a distribution of randomly chosen points.  If you do mean that then A, B and C are all saying the same thing, because the occurrence of blocks is a poisson distributed random process.  The time a block is created is as good a chosen time as any.  Thus I would expect 1 minute = 1 minute = 1 minute.

Though the way he wrote it sounds like it would be valid when watching the past of created blocks too. Or when he chose a time in the future then the blocks that are solved around these points in time, when the time went time finally, would make it correct too.

Maybe he meant it different but if that statement is only true theoretically then it might have stated.

[smooth]

Does this equivalence make Dooglus's "random point in time" equivalent to "the time a random CLAM block is generated"?

It sounds like no, because my set of times contains x members, where x is the CLAM block height.  Dooglus's set of times has an unbounded quantity of members. 

You're getting warmer

[bobboooiie]

Funny thing about Poisson Processes: Every day you don't stake, you still have 100,000 days to go.

Here's a fun thing:

Pick a random point in time, then:

A) the average amount of time from that point to the next CLAM block is 1 minute
B) the average amount of time from that point to the previous CLAM block is also 1 minute
C) the average time between CLAM blocks is also 1 minute

Wouldn't you expect A + B = C? Yet A, B, and C are all 1 minute.

7 kilometers!

[tittiecoiner]

http://blog.cryptsy.com/

– Update 2016/01/19 10:08pm –
The following wallets have been opened for withdrawals:
* Clams

Time to get them out, in case someone still has some CLAM sitting there