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current events death mathematics numbers politics probability science statistics trust

Why Stories Circulate about Covid-19 Deaths

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I’ve seen several posts on Facebook claiming that deaths of relatives or friends have been falsely attributed to covid-19 when in fact they were due to some other cause. These anecdotes represent a misunderstanding of the way statistics work and how data for statistics is collected. Of course, researchers want as accurate a count as possible for the number of deaths caused by Covid-19. But that kind of accuracy is harder than it sounds.

At first researchers were counting only deaths where the person who died had tested positive for Covid-19. They soon realized however, that they were under-counting the number of Covid-19 deaths. How did they realize that? They knew what the death rate in a particular place was prior to the pandemic. For example, if a city typically had 1,000 deaths in 30 days, and suddenly the number jumps to 3,000 but only 1,500 of those were due to patients who tested positive for Covid-19, then that left 500 deaths unaccounted for. So researchers decided to broaden the criteria for recording deaths as attributable to Covid-19. They decided to included deaths where symptoms were similar to those caused by Covid-19. They also included deaths even when the patient tested negative.

Why would someone who tested negative for covid-19 still be listed as a victim of it? Testing is not 100% accurate. Data on accuracy of the most widely used Covid-19 test is not publicly available, but some estimates range as high as 30% for false negatives, meaning that 3 out of 10 people who test negative for the disease actually have it. Even with a test that is 100% accurate under ideal conditions, real-world conditions can skew results. Many conditions can affect the amount of virus in a specimen collected by a swab. The most widely used test has close to a 100% accuracy for positive results, the the accuracy for negative results is uncertain and can vary depending on many factors. This is why some people who have died after testing negative for covid-19 are nevertheless listed as victims of covid-19. As long as they had symptoms consistent with the infection, they might very well have covid-19 listed on their death certificate. Of course, casting a broader net for data also means that there will be instances of people being listed as having died from covid-19 who actually died of other causes. Researchers make every effort to ensure this does not happen, but no procedure is foolproof. However, if the number of deaths identified as having been caused by Covid-19 matches the uptick in deaths overall, then it’s a pretty safe assumption that the data is pretty clean.

Because many people are suspicious of our government or the media or liberal elites—none of which are actually sufficiently monolithic to carry off a genuine conspiracy—and of expert authority in general, these types of stories gain currency on social media. Some may be true, but they usually do not contain sufficient detail to validate them. Even if they are true, they are generally offered by people who are not experts in determining cause of death.

So before you share one of these anecdotes about a suspicious Covid-19 death, consider not just whether it is true, but also whether it undermines the very institutions we have put in place to help us deal with infectious disease epidemics. While there are plenty of politicians ready to make hay out of crisis events, the experts and researchers who do the actual work genuinely care about producing good quality studies that advance our understanding of the virus and how it spreads. They are not out to get you.

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infinity mathematics numbers set theory

What Infinity Means to Me

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I have a habit of reading no matter where I am or what else I am doing. I read at my computer. I read on my phone. I read while waiting at the doctor’s office. I read in the bathroom. Lately I’ve been reading a book by Stanley Fish called How to Write a Sentence: And How to Read One. Several times he makes the claim that the number of sentences one could write is infinite. This is demonstrably untrue. The number of unique sentences one could write is certainly very large, but no mathematician would ever mistake a very large number for infinity. The fact is you can’t get an infinite collection of things using only finite collections for building blocks. For example, no matter how many molecules remain to be discovered, the total number of possible molecules cannot be infinite because the number of atoms is finite, and molecules are made up of atoms. In the same way, the collection of words is finite, so the collection of sentences (which are made up of words) must also be finite, even if we place no particular limits on the length of the sentences except that they must terminate.

The concept of infinity arises in set theory. A set is a collection of things together with a rule that tells us whether a thing belongs to the set. A set can be an explicit list: {coffee, butter, flour, sugar, tomatoes, eggs}. In this case the rule is: “If the thing is on the list, it is part of the set. Otherwise it is not.” Or a set can be defined by a rule: the set of all cats in the world. To see if something is in this set, we need only answer two questions: 1) Is it a cat? 2) Is it in the world? (We might also need to decide whether “cat” refers only to “small, domestic cats” or also to “big cats” such as lions, tigers, ocelots, pumas, bobcats, cheetahs, or other animals of the cat family, but we could in principle make such a decision ahead of time and use it to determine which things belong to the set and which do not.) One question we could ask about a set is how big it is. How many members does a set have? In the case of my shopping list, we can just count the items in the list and see that there are 6. In the case of cats in the world, we could in principle count the cats, but doing so raises a number of practical considerations. For example, how do we keep from counting the same cat more than once? How do we account for cats that are born or die while we are doing the counting? There may be 600 million small cats in the world. Counting them is going to take some time. Nevertheless, we know that having counted them, the number we obtain will be a natural number. We can say whether it is larger or smaller than the number of people in the world or the number of dogs in the world. We may not know exactly what the number is, but we know that it is a number we could count to if we counted long enough.

One of the things we know about the universe is that it is finite. It’s not hard to see why. If the universe were infinite, then the number of stars would be infinite; the number of galaxies would be infinite; the gravitational pull would be infinite; the light energy produced by all those infinite stars would be infinite. The night sky would be white if by some anomaly in the physics of the universe the earth were still pretty much as it is now. All of our experience of the universe is with finite things. Nothing is infinite. Everything is enumerable—at least in principle.

Infinity is an acknowledgement that some sets have no boundary on the number of elements they can have. However, those sets are themselves ideas only; they do not represent material objects.

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