One of the questions I like to pose in my classes is “how do you know?”  Doing analysis of data and possible decision leads to lots of wild speculation, and this question sometimes brings us back to recognizing that widely held theories are actually quite tenuous.  One observation can bring down a whole theory, a “black swan” event.  I like to use examples from physics, even though I am not a physicist, because I find that students often think that we “know” stuff there.  Science is settled, even if other areas are not.

Here is an interesting (to me) article about measuring light and comparing the measurements to accepted physical theories.  At the end, something to think about:

There’s also a possibility that the explanation could be even more far-reaching, such as that the universe is not expanding and that the big bang theory is wrong.

How certain are you of the things you know?

First, I have not followed up on the reference in this Instapundit blog post, so I do not know whether this is really the way the British Met Office really computes average temperatures:

In fact, the Met still asserts we are in the midst of an unusually warm winter — as one of its staffers sniffily protested in an internet posting to a newspaper last week: “This will be the warmest winter in living memory, the data has already been recorded. For your information, we take the highest 15 readings between November and March and then produce an average. As November was a very seasonally warm month, then all the data will come from those readings.”

But suppose for a minute that an average for a whole season (year) really is fifteen days, and that the highest fifteen all (most) came from November. Would that really represent the average for the winter? Can you think about why they would not use every day’s reading from November through March? Should they use just the high for the day, or the high and the low for each day? And where should the reading come from? How many locations around England would be enough for what would seem like a good average calculation? What if averages in the past were computed differently? Could you make comparisons?

Average seems like such an easy concept – but it often is quite tricky. To say nothing about trying to understand the variability of temperatures (do they compute standard deviations?)

For example, the fifteen day record could occur in a season where the other one hundred and thirty five days were pretty cold…

I am naturally somewhat of a skeptic, but it is hard to not read something and think about how smart the scientists are, and how much they know, and what will soon be possible. One of the things that is really interesting is brain research. Suppose we could know how we work?

All kinds of new tools allow researchers to “watch” your brain work. Or can they? How do they “know”?

Here some interesting reading about the difficulties in measuring, knowing and statistics.

Here is another that makes you think twice when we assume that science is a clean process that follows a straight line to the truth, getting it right along the way.

And here’s a cartoon view of how this works (or doesn’t work).

This cartoon site has quite a bit of “geek” humor, so I like it. It also has an interesting feature where if you move the mouse over the cartoon, a hidden message appears. This one has a comment about “the mother of all sampling biases.” It may not seem funny, but it is a really great example. Some of his other cartoons are pretty good. This one makes me wonder about teaching statistics.