4 ms·

Given that the blockchain can split at any time with a probability based on incentive that approaches infitesmal values as chain size goes to infinity, the bloc

Given that the blockchain can split at any time with a probability based on incentive that approaches infitesmal values as chain size goes to infinity, the blockchain is not even eventually consistent. It is never consistent, only probabilisticly consistent.

brudgers 10y ago
Numbers that fool the Fermat test are called Carmichael numbers, and little is known about them other than that they are extremely rare. There are 255 Carmichael numbers below 100,000,000. The smallest few are 561, 1105, 1729, 2465, 2821, and 6601. In testing primality of very large numbers chosen at random, the chance of stumbling upon a value that fools the Fermat test is less than the chance that cosmic radiation will cause the computer to make an error in carrying out a "correct" algorithm. Considering an algorithm to be inadequate for the first reason but not for the second illustrates the difference between mathematics and engineering. https://mitpress.mit.edu/sicp/chapter1/footnode.html https://mitpress.mit.edu/sicp/chapter1/footnode.html
kens 10y ago
What the probabilistic approach misses is that the blockchain can split for other reasons, so the exponentially small chance of inconsistency is irrelevant. For instance, in 2013 the blockchain was split for 6 hours (24 blocks) due to a block with more than 10,000 transactions that different software versions handled incompatibly. The other thing the probabilistic discussion skirts is that even with an exponentially small probability, you need to wait inconveniently long. A Ω value of 6 corresponds to 1 hour. To get down to "alpha particle" levels of probability you've got a much longer wait.
- goldenkey 10y ago
  How is the nonzero probabilistic chance of a split not a problem considering that vendors are relying on the durability of transactions that may appear in one chain but not the other?

brudgers 10y ago

Numbers that fool the Fermat test are called Carmichael numbers, and little is known about them other than that they are extremely rare. There are 255 Carmichael numbers below 100,000,000. The smallest few are 561, 1105, 1729, 2465, 2821, and 6601. In testing primality of very large numbers chosen at random, the chance of stumbling upon a value that fools the Fermat test is less than the chance that cosmic radiation will cause the computer to make an error in carrying out a "correct" algorithm. Considering an algorithm to be inadequate for the first reason but not for the second illustrates the difference between mathematics and engineering. https://mitpress.mit.edu/sicp/chapter1/footnode.html https://mitpress.mit.edu/sicp/chapter1/footnode.html

kens 10y ago

What the probabilistic approach misses is that the blockchain can split for other reasons, so the exponentially small chance of inconsistency is irrelevant. For instance, in 2013 the blockchain was split for 6 hours (24 blocks) due to a block with more than 10,000 transactions that different software versions handled incompatibly. The other thing the probabilistic discussion skirts is that even with an exponentially small probability, you need to wait inconveniently long. A Ω value of 6 corresponds to 1 hour. To get down to "alpha particle" levels of probability you've got a much longer wait.

goldenkey 10y ago
How is the nonzero probabilistic chance of a split not a problem considering that vendors are relying on the durability of transactions that may appear in one chain but not the other?