It is quite astonishing to me how much attention some people pay to their diets, even if they have no medical condition that requires them to be careful about what they eat or drink. This feeling that certain diets can be the pathway to good health and longevity has been exploited by some to promote various fads that can, in fact, be dangerous. This article describes some popular fads that one should be very wary of.

This article warns that excessive fears about food, that come under the heading of ‘clean eating’, can lead to obsessive behavior and all manner of problems.
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I was a little surprised at the length of the comment thread in the post about the logic puzzle involving the monk Gaito going up and down a hill. On the one hand, I thought that there were some excellent explanations of why there had to be at least one instant where the monk was at the same location at the same time. These involved visualizing the situation in slightly different ways, such as instead of having one monk go up and down on two different days, having two monks going up and down on the same day or using graphs or films and so on.

But clearly these arguments were not persuasive enough for some and I have been trying to think why this might be so. In my teaching experience, it is often the case that what seems obvious to you as a teacher is by no means so to the student. It is no use repeating the same explanation more slowly or (worse) more loudly or (much worse) exasperatedly. There is clearly some opposing argument that the student finds persuasive that makes them reject your argument and yet they may not be able to identify and articulate what it is. Instead they feel that there must be some flaw in your reasoning that they cannot put their finger on. It is more fruitful as a teacher to try and figure out what their argument might be, rather than reiterating your own.
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When the Earth first formed into a solid sphere with an atmosphere, that atmosphere was deficient in oxygen. The question of when and how the planet became oxygen rich is an interesting and important one and recent research challenges some old ideas about the earliest appearance of oxygen.

The “Great Oxygenation Event” that infused the gas into our atmosphere is commonly thought to have occurred around 2.4 billion years ago, when a rise in cyanobacteria released a huge amount of oxygen through photosynthesis. But it’s been difficult to get any more precise in terms of dating the first appearance of this life-giving gas; after all, how are scientists supposed to detect such a small quantity of oxygen from so long ago?
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On March 11, 2020, the World Health Organization declared Covid-19 to be a global pandemic. In the two years since then, we have passed one grim milestone after another. As of yesterday, there have been 483 million cases worldwide or 6.1% of the total population of 7.9 billion. There have been a total of 6.2 million deaths.

When one looks at the per capita death rates, apart from Peru (which has the highest rate), Brazil, and Chile, the rest of the top 20 countries for cases are in Europe or the US. In fact, the highest ranking country outside Europe and the Americas is at #35 with Tunisia. A similar pattern holds for infection rates.
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The covid-19 pandemic is going to be a rich source of data for how to deal with any future pandemics. The prevalence and degree of severity of the disease has varied widely across the globe, as have the ways in which various countries responded to it, and this has given rise to so-called ‘natural experiments’, those in which one can isolate and study the effects of individual factors without having to actually do experiments.

One of the firmest lessons is the importance of vaccinations for everyone but especially the need to vaccinate those segments of the population that are most likely to suffer adverse effects and death. In the case of covid-19, it was the elderly and the immunocompromised who were most at risk.

But there is also the question of how far to go with trying to isolate regions in order to keep the virus out of the country. The countries that practiced severe lockdowns and strict border controls (such as China, New Zealand, and Hong Kong) were initially able to keep the numbers extremely low while many other countries were suffering badly, but now the situation seems to be reversed in that the previously affected countries are seeing a decline while those initially low case number countries are seeing a spike.
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Probability can be deceptive. The concept sounds easy to understand and we glibly use the ideas in everyday life but there are many subtleties involved. Given how important probabilistic ideas are in life, some have suggested that it be introduced into school mathematics curricula much earlier than it currently is and discussed in more depth.

One subtlety can be highlighted by this example. Suppose that you read about a new study that finds that by taking some measures, you can reduce the risk of stroke by 50%. Should you adopt those measures?

To make a decision you need to weigh the benefit against the costs, which in this case may be that the measures involve taking medications that have rather serious side effects, or that the regimen involved is arduous, or that it is very expensive. But even taking those into account is not enough to decide because you need to know another key piece of information and that is the absolute risk numbers.

The relative risk is what is usually reported and quoted in the media. It is obtained by comparing the results of the test group with the control group. So if the test group has five positive cases and the control group has ten, then the relative risk reduction is 50%. But this ignores the importance of sample size that determines the absolute risk. If the sample size had been 10,000, the absolute risk would have dropped from 0.1% to 0.05%.

Paula Byrne, one of the authors of a recent study on the benefits of taking statins to lower cholesterol, says that focusing only on relative risk does not give enough information to make an informed decision.
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