I don't know what he means by "inherent in the data itself" but "noise" is random and uncorrelated. Analog systems are noise limited, but digital systems are interference limited and interference whilst it contains noise also contains a great deal of correlated information that a clever system can filter away.
Taleb's thesis that too much data is the problem cannot be correct. It is too little filtering.
Five clocks is getting damned complicated. Twenty, I suspect you're well into the billions. But I'm just an artist. Let someone else do that math.
The math is actually very simple when you're asking for all possible combinations. Each clock is either included in your selection, or it isn't - one of two choices. So for 20 clocks, there are exactly 2^(20) combinations (2 multiplied by itself 20 times, or 1,048,576).
The more frequently you look at data, the more noise you are disproportionally likely to get (rather than the valuable part called the signal); hence the higher the noise to signal ratio. And there is a confusion, that is not psychological at all, but inherent in the data itself. Say you look at information on a yearly basis, for stock prices or the fertilizer sales of your father-in-law’s factory, or inflation numbers in Vladivostock. Assume further that for what you are observing, at the yearly frequency the ratio of signal to noise is about one to one (say half noise, half signal) —it means that about half of changes are real improvements or degradations, the other half comes from randomness. This ratio is what you get from yearly observations. But if you look at the very same data on a daily basis, the composition would change to 95% noise, 5% signal. And if you observe data on an hourly basis, as people immersed in the news and markets price variations do, the split becomes 99.5% noise to .5% signal. That is two hundred times more noise than signal —which is why anyone who listens to news (except when very, very significant events take place) is one step below sucker.
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