Computer cameras as spying devices

My attention was drawn to this newspaper article about how more and more people are covering up the cameras that are in their computers out of concern that other people could, unbeknownst to them, actually turn them on and spy on them. This fact has been known for some time to computer security experts but was given greater publicity by Edward Snowden as part of his expose of how the NSA and other government agencies spy on people.
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Using math puzzles to illustrate the nature of science

(As I mentioned some time ago, I am working on my next book that is tentatively titled The Paradox of Science. From time to time, I will try out ideas from it on the blog, suitably modified to make the blog posts self contained. Readers get the benefit of a sneak preview and I hope to get feedback from readers as to clarity, correctness, style, etc. Note that the book is aimed at the interested layperson and not the many experts who read this blog so put yourself in their shoes when reading. This post is the first of such offerings. Enjoy!)

The website Fivethirtyeight has a weekly feature called The Riddler where puzzles of a mathematical sort are presented and the solution given the following week. Here is one such problem stated in its entirety:

Complete this series:

10, 11, 12, 13, 14, 15, 16, 17, 21, 23, 30, 33, …

I want to use this simple purely mathematical puzzle to illustrate an important insight about science. I will give the solution below the jump and then discuss the relation to science.
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Ethical issues with experimental drug treatments

The US has a pretty strong regimen for getting drugs approved, a system that has great credibility after it kept out the nausea and morning sickness combatting drug thalidomide that in the 1950s wreaked havoc on babies in other countries. The gold standard for new drugs to be allowed to be prescribed is, as I understand it, that they have to show that they do not pose significant risks and also undergo double-blind clinical trials on humans that demonstrate that they work better than a placebo. The process is long and expensive.
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Slowing down lightning

High-speed photography enables us to see the beauty of some of nature’s most spectacular effects, such as lightning strikes. Ningyu Liu at the Geospace Physics Laboratory at the Florida Institute of technology recorded lightning during a storm. He filmed it at 7000 frames per second and with the playback speed reduced to 700 frames per second, the result is quite beautiful.
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Welcome to Florida! But please don’t get eaten

When he was the weekly humor columnist for the Miami Herald, Dave Barry found the area’s weirdness a fertile source of material, writing about the venomous snakes and other wildlife that he would find in his backyard. One can only imagine what he would have done with the reccent news that three human-eating crocodiles that are native to the Nile river in Egypt have now been found in that state.
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How to cut a cake fairly into N pieces

Suppose you have N people and one cake. How can you cut the cake such that each person is satisfied that the pieces have been distributed fairly? This is an old problem that Martin Gardner wrote up in his column for Scientific American and in the case of two people it is quite simple: One person gets to cut the cake into two and the other person gets to select the piece they want. (But see later for a problem with this.)

But what if there are more than two people? Below the fold, I give Gardner’s explanation on how to do it, starting with the case where N=3, quoted by Walter Stromquist in an issue of The American Mathematical Monthly.
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