The Law Of Small Numbers

I spent most of yesterday where I ended the night before.  Spending an enjoyable day in the company of friends (including at least a little time in the evening with some of those I had eaten dinner with on Saturday evening [1]) does not always make for a blogworthy day, though.  There is only so much one can say about trying to avoid mud puddles or observing the new paint on a chicken cook, as much as I enjoy chicken, or watching someone show off part of their impressive arsenal of weapons modified to meet the technicalities of gun laws.  Be that as it may, once I had finished writing about my lengthy Sabbath and took a quick shower, I was sufficiently ravenous, and the hour was sufficiently late, being more than one hour after noon on a day where I lost sleep, that it was time to head to an enjoyable lunch at a neighborhood pub & grub just down the hill.

While eating perfectly serviceable but not particularly spectacular food, certainly nothing worth blogging about in detail, we mused on the fact that this particular restaurant used to be far less expensive before a remodel induced by a kitchen fire.  To give but one example, they used to have a Friday prime rib special for $10, which is not $18.  This conversation led into a discussion about the other restaurant in the area, which happened not to have been open since a kitchen fire of their own.  Given that this particular company is where I spent my most dangerous Thanksgiving ever due to a stove fire [2], I was led to ponder the problem of kitchen fires and how common they are.  Admittedly, two restaurants in a small area is not a big sample size, but the odd occasion of kitchen fires requiring extensive repairs that either put restaurants out of business or led them to drastically increase the price of food to recoup the expenses would easily prompt the question of how common such kitchen fires are anyway.

According to the National Fire Prevention Association [3], there were an average of 166,100 kitchen fires per year where the fire department was called.  This does not include those cases where, like in the Thanksgiving fire, the family was able to successfully fight the blaze themselves without the need for assistance from the fire department.  At any rate, 166,100 fires per year, while a large number, is a very small percentage of the homes and restaurants in the United States, given that there are over 125 million households in the United States [4] and over 600,000 restaurants [5].  Given such numbers, kitchen fires must be remarkably rare in restaurants, so for an area to go 2/2 in having substantial damage from kitchen fires over the span of a few years suggests either immensely bad luck, active sabotage, or remarkable negligence.

It is hard to distinguish between these without knowing the motives of the people involved and the contexts of the disasters.  What does appear likely, though, is that we are dealing with a situation involving small numbers.  Many people are at least passingly familiar with the law of large numbers [6], which posits that there is safety to be found in having large enough numbers that the risk to any one particular person is less.  The inverse would suggest that there is a great deal of risk in small numbers, and that having small numbers increases certain problems related to incidence, such that any risk for any disaster that happens where there are small numbers is appreciably greater than the equivalent risk for a randomized large number.

It is not hard to see why this may be the case.  A genetic mutation, nearly always bad, is not so harmful in a large number, where its incidence is likely to be rare and where it will therefore affect few people.  The same mutation, though, in a small population, is likely to be spread rapidly on account of the fact that there are fewer possible pairs, more of which would contain the mutation, especially when considering the passage of time.  We may at least hypothesize that the same would be the case when we look at restaurant fires, in the knowledge that remoteness and smallness would put areas more at risk because such areas would be further from help than less remote areas, and that trouble and distress in small communities are likely to place those areas under more stress than equivalent distress in areas where there are more people and more institutions around.  We can draw from this a variety of conclusions, an exercise I largely leave to the reader.

Would I would like to comment on is the fact that widespread mistrust for institutions has led to a drastic increase in small numbers over the past generation or more.  Populations in the United States fled cities first to suburbs and then to more remote exurbs and rural areas in the hope of escaping burdensome control and enforced intimacy with those they disliked.  Believers fled large mainline religious institutions for local nondenominational churches or “megachurches” that lacked a large institutional bonding with millions of others.  And so it goes.  Ultimately, large numbers of people can only be joined together by some sort of love and mutual regard or some kind of external force.  And our love has grown cold and our institutions lack the legitimacy to force us together when we wish to be apart.  What then are we to do but face the ravages of the law of small numbers?






[6] See, for example:

About nathanalbright

I'm a person with diverse interests who loves to read. If you want to know something about me, just ask.
This entry was posted in Christianity, Church of God, History, Love & Marriage, Musings and tagged , , , . Bookmark the permalink.

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