Are you suggesting that the high positive correlation of, say, corn and Dow (as mentioned above) over the last 180 days is anything but a random occurrence? Or did you mean something else when you said: The basic point of my reply wasn't about "the books" or any statistical significance testing. This is about a large correlation matrix (1,000+ elements) across a variety (here 35) of diverse asset classes and instruments. Given those two facts, you cannot not have multiple instances of a correlation near one of the two extremes, 1 or -1. And?... And many of those instances will be random (contrary to your statement); an accidental fluke; of no particular meaning, relevance or use, in trading, investing or any other area. If you are going to make any use of that correlation -- to draw any valid inferences from it -- then that's exactly the question you should ask. Otherwise, it's garbage in, garbage out.
I think what the poster meant is if you looked at a large number of 180 day periods the correlation calculated for each sample would not have been as high as the current one; thus he used the word "random" maybe spurious is a better word.
In my experience, when using limited data, it is very useful to use a "null hypotheses" analysis. In this case, the null hypotheses is the data represented in the graph itself. One would need several more data sets of past 180 day periods, or at very least, a break down of the existing data into 30 day periods in order to statistically quantify. I predict, even with a breakdown of existing data, the data will minimalize the high correlation of DOW/Corn. Using additional historical data, the high correlation will be refuted, imo. Therefore, it is a marginal probability... the high correlation is statistically insignificant because the correlation does not need to exist for the probability of such movement to exist. My teacher would be proud.