Quote from: xulescu on October 02, 2014, 05:35:33 AM

For the fourth time, the burden of proof rests on you to prove material change. You cannot prove lack of material change in a stochastic environment because you need infinite data. That is not the case with proving change.

Why do you keep attacking me with strawmen?

I never claimed an attack! I wanted to analyze the rareness of the cited event. I didn't even claim it was abnormal.

You conflate investigation with intent. You desire to make an argument where there was none, because you assume any investigation is pro-attack. Why this immense emotional resistance to probing and the scientific method of peer review? Could it be you have some vested interest? (Rhetorical question)

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Of course the probabilities are not 0.5. But they also don't matter much. Since both my semantic simile and your argument assume independence, order does not matter. Thus all permutations are in the same class of rarety.

Each trial in a coin toss has a 0.5 probability shared between two outcomes. Chaining independent trials does give rarer probabilities for certain permutations. Each trial in the Poisson distribution is an infinite range of probabilities shared between infinite possible outcomes. Thus there is a much higher stratification possible within just one trial or a few trials than is possible with a coin toss. Thus we are able to see very, very unlikely events with only a few trials, unlike for a coin toss. Thus we find that the majority of the events are clustered in certain patterns over just a few trials that aren't so rare, and if we see an outlier from that occurring much more frequently then we can posit an abnormality (assuming the Poisson distribution is a predictive model of normality). Thus I asserted your analogy is inapplicable.

You are attempting to claim that distribution functions don't matter and thus the distribution of permutations between different distributions are the same. FAIL.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Furthermore, if only counts of "short" vs "long" gaps matter, then instead of x seconds times 8 + y seconds times 4 you also need to include small deviations. Such as, for example, x-1, x+1, x times 6 + y times 4, and all the permutations of each of these. So you are integrating over all partitions on 12 elements, which is a gigantic set when you generalize enough to learn the blockchain in any meaningful way. The blockchain has too little data to believe your statement with even 60% confidencence. We're talking 0.1 sigma deviations here and a combinatorially monstrous set, with only a quarter of a million of data points. Not gonna happen.

On the contrary, my position is that given the amount of entropy there is in the blockchain so far, and adding time dependence to the combinatorial mess (because independence is false), we cannot say that there is something wrong with meaningful certainty.

You are attempting to model block occurrences via regression assuming you have no known distribution. Thus of course you need a lot more data to find a model. You assume the Poisson distribution is incorrect, but have you proven it? Even so, my argument wasn't initially about whether the Poisson distribution is a useless model. I was only arguing what it would say if it is the chosen model.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Finally, over all this academic modelling exercise that we went through, the reality is, as I mentioned in my first post and smoothie detailed, that even if you were right on the modelling, what we know about how timestamps work and how they are somewhat adversarially arbitrary for you as the modeller, your conclusion holds no epistemic water.

And timestamps are how we compute difficulty, which is intimately related to TW-like attacks. So if the timestamps are unreliable, that gives me a lot of confidence that we are immune to a TW attack. I actually have some ideas about how to make timestamps reliable and no that doesn't mean relying on an NTP without network hiccups.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

You are right on the Maths. You are wrong on many levels on your modelling. Even if you were right on the modelling, you are still wrong on what conclusions you can draw from the results.

I never asserted I had the correct model. I was analyzing what the Poisson model would say.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Your argument is "something could be wrong".

No it wasn't. My argument was it might be more rare than once per hour. My argument was neatly compartmentalized, but you tried to build a strawman to attack me with.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

My counterargument above is "even if that was the case, you don't have enough entropy to draw that conclusion".

In your regression yes, but in the assumed Poisson distribution incorrect.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Smoothie's corrolary is "even if you are right, it doesn't make much of a difference".

We don't know that yet. You guys are quick to jump to conclusions.

Quote from: xulescu on October 02, 2014, 05:35:33 AM

Thank you for responding calmly earlier and compelling me to articulate my position.

I am trying but when you keep rebuilding the same strawman and you embed your rebuttals as bold text in my quoted text making it difficult for me to quote you, its FUBAR.