Correlations: Plausible or implausible, NONE prove causation

My critique of confusing correlations with causes (60 MINUTES on aging — correlations or causes?) brought a number of comments, including a link to a boingboing piece, “Spurious correlations: an engine for head-scratching coincidences”  with an illustration of a correlation that is obviously not a cause-effect relationship:

This came from a website  with software that can generate correlations on request from a large database. Many other examples are offered of correlations that are obviously meaningless, for instance:

Far too many people and institutions perpetually fall into the trap of taking correlations as causation. The error is pervasive in statements and publications about medical science and practice from official agencies and from doctors and researchers, and the media perpetually fail to debunk such statements.

So the Spurious Correlations website is a valuable tool
for reminding people never to assume that a correlation has a causal basis.

But I would like to add a couple of comments.

1. Our intuition about what a “correlation” is differs from how numbers like the 0.947091 in the example above are calculated. As the website points out in its “About this page” (whose link is anything but prominent), “there are better ways to calculate correlation than I do here” .
The website uses what is perhaps the most common formula, “a simple Pearson’s correlation coefficient”. That’s also used in the Microsoft Excel CORREL formula. I first realized how different the result of that can be from an intuitive sense of correlation when an article claimed a geographical correlation between HIV and AIDS for which the actual data seemed to me to show “obviously” no correlation (pp. 110-2 in The Origin, Persistence and Failings of HIV/AIDS Theory).
An informal tutorial from my friend Jack Good  set me straight. Everyone should beware that what might seem like quantitatively very good correlations, with numbers like 0.75 or more, may not signify what our intuition says about how good or bad the correlation is.
(And everyone should beware of the accuracy implied by numbers like 0.947091. All too many publications show such numbers, copied from a computer, that imply an accuracy to 6 significant digits, 1 part in a million. Rarely are more than two figures warranted, in this case 0.95.)
2. The most important caveat, though, is that the Spurious Correlations website features correlations that are obviously absurd and not reflecting any causal relationship. In the real world, however, considerable real damage is done all the time because

correlations that look plausibly reflective of a causal relation
are mistakenly taken to reflect actual causation.

That happens pervasively in medicine. Correlations between blood pressure and heart attacks, for example, led to designating blood pressure as a “risk factor” for heart attacks, interpreted mistakenly as high blood pressure constituting an actual risk of causing heart attacks, and using medication to lower blood pressure when in actual fact there is no evidence that high blood pressure causes heart attacks (or strokes) — see “Evidence-based medicine? Wishful thinking”  and “Seeking Immortality? Challenging the drug-based medical paradigm”.
All sorts of shibboleths about HIV/AIDS are treated as fact by media and public just because they seem plausible for a sexually transmitted infection, yet there evidence is plain that neither “HIV” nor “AIDS” is infectious and that they are not correlated with one another. (Correlation never proves causation; but lack of correlation is strong evidence against causation and places heavy burden of proof on anyone claiming causation.)
So too with “global warming”. Given all the doubts about human-caused global warming, for instance that carbon dioxide in the atmosphere has continued to increase dramatically during the last ~15 years without discernible increase in temperature, global-warming and environmentalist activists have succeeded in making the dogma one of (unfalsifiable) “climate change” instead of warming, and pundits galore hold forth about how “climate change” has brought more extreme events that are increasingly extreme — which seems so plausible, until you realize that this is mere speculation and not a reflection of known historical events; and that one could just as plausibly speculate that, as temperature rises, ocean and air currents become stronger and will tend to even things out and decrease the likelihood of extreme events.

Correlations never prove causation
and that needs to be emphasized over and over again,
the more plausibly causative a given correlation  appears to be.