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 The [[signal]] depends on a theory of the game,  Otherwise the “relationship” between the two discrete transactions is arbitrary. Without a theory, everything is [[noise]].
 =====The theory-dependence of signal=====
-If given events are truly “independent” — in a first order sense, they are: the participants in the later trade do not know who or where the participants in the earlier even are, let alone what their motivations for trading were — then a “trend” we draw between them is, more or less, meaningless. All that is left is mathematics.
+If events are truly “independent” — in a first order sense, they are: the participants in the later trade do not know who or where the participants in the earlier even are, let alone what their motivations for trading were — then any “trend” we draw between them beyond their distribution is, more or less, meaningless. All that is left is mathematics.
-But we ''have'' a theory, so draw the line all the same. We make assumptions about the homogeneity of all market participants: we assume all have similar price information, and that all are propelled by the same essential economic rationalism: you don’t sell things you expect to do well, and you don’t buy things you expect to do badly.
+But we have a theory, so we draw the line all the same. We assume the market is homogeneous, that all participants have similar price information — those who have more are forbidden to trade — and that all are propelled by the same rationale: you don’t sell things you expect to do well, and you don’t buy things you expect to do badly.
 =====Private narratives wash out=====
-Each investor’s private motivations, and opinions, may be nuanced and personal — how is the rest of its portfolio positioned, what local risks is it especially sensitive to — but these idiosyncrasies cancel out in a large sample — they are like the [[Brownian motion]] of molecules in a [[nice hot cup of tea]]. They are reversions to the [[entropy|entropic mean]]; baseline white noise — so we can disregard them. Which is just as well for the complexity of our models. Until it isn’t.
+Given these assumptions, across the market investors’ private motivations, opinions, theories and idiosyncrasies cancel out — they are like the [[Brownian motion]] of molecules in a [[nice hot cup of tea]]. They are reversions to the [[entropy|entropic mean]]; baseline white noise — so we can disregard them. Which is just as well for the complexity of our models. Until it isn’t.
 Put another way: although the “interconnectedness” of similar transactions means they do ''not'' have the quality of independence that [[normal distributions]] require, most of the time it’s close enough: the information is chaotic — as traders say, “noisy” — in the immediate term, here the dissimilarities between trader motivations are most pronounced, but over a large aggregation of trades and a longer period a “signal” emerges. This is what [[Black-Scholes option pricing model|Black-Scholes]], volatility and convexity models track: as long as all traders all use the same aggregated market information — and the market works hard to ensure they do — a “normal” probabilistic model<ref>I am working hard not to use the intimidating term [[stochastic]]” here by the way.</ref> works fairly well. It’s not a bad ''model''.