Invoice literacy in the Middle East

Why our minds do not perceive probabilities intuitively

by Michael Shermer

Have you ever reached for the phone to call a friend but he called you earlier? What are the chances of that happening? They are certainly not high, but the sum of all probabilities is equal to one. If given enough opportunities, even unusual phenomena, even those that seem like a convention, will occasionally occur.

Let's define a miracle as an event that has a million to one chance of happening (intuitively this sounds like a small enough chance to justify the definition). Let's also determine that data flows to our senses during the day at a rate of one bit per second, and let's assume that we are awake 12 hours a day. We therefore ingest 43,200 bits of data per day, or 1.296 million bits per month. Even if we assume that 99.999% of these bits are completely unimportant bits (and therefore we filter and forget them forever), we will still be left with 1.3 "miracles" per month or 15.5 miracles per year.

Thanks to our "confirmation bias", which causes us to look for, and find, confirming evidence for things we already believe and to ignore or dismiss contradictory evidence, we will only remember those amazing coincidences and forget the vast and meaningless sea of ​​data.

We can do a similar quick calculation to explain dreams that predict death. The average person dreams about five dreams a night, or 1,825 dreams a year. Even if we only remember 10% of them, their number per year reaches 182.5. Three hundred million Americans therefore remember 54.7 billion dreams a year. Sociologists claim that each of us knows an average of 150 people fairly closely, so the social dating network in the United States has 45 billion mutual connections. The death rate in the US is 2.4 million deaths per year, so it is inevitable that some dreams out of the 54.7 billion dreams that Americans remember will deal with the death of some people out of the 2.4 million who died among the 300 million people in the US who maintain 45 billion social relationships. In fact, it would be a real "miracle" if no one had a dream predicting death that would come true.

These examples show the power of probabilistic thinking to trample our intuitive sense of numbers, or the phenomenon I call "folk invoice literacy". Folk arithmetic literacy is our natural tendency to perceive and calculate probabilities incorrectly, to think casually rather than statistically and to focus and remember only short-term trends and only sequences of small numbers. We notice a short streak of cold days and ignore the long-term global warming trend. We are amazed by the recent downturn in the stock market and the American housing market and forget the rising trend line in the last half century. Trendlines that zigzag like the teeth of a saw are actually an instructive example of mass arithmetic: our senses are trained to focus on the rising or falling segments while the general direction of the saw almost disappears from our sight.

Our day-to-day intuition is so often mistaken because we evolved in a world that evolutionary biologist Richard Dawkins called the "middle world" - a world that lies halfway between the short and the long, between the small and the large, between the slow and the fast, and between the young and the ancient. For personal reasons I prefer to call this world "Middle Earth". In the middle land of space, our senses developed to perceive objects of medium size - between grains of sand, for example, and mountain ranges. We are not equipped with senses that allow us to perceive atoms and bacteria, on one side of the scale, nor galaxies and expanding universes on the other side. In the middle land of speed, we are able to recognize bodies moving by walking or running, but we are unable to perceive the slow creep of the continents and glaciers and the dizzying speed of light. The dimensions of time in our Middle Earth, which extend from the psychological "now", which lasts three seconds (according to psychologist Stephen Pinker from Harvard University), to several decades of human life, are dimensions too short for us to witness evolution, the migration of the continents or long-term climate changes. The popular numeracy literacy in our middle country makes us pay attention and remember only short-term trends, only significant coincidences and only personal stories.

Michael Shermer is the publisher of the journal Skeptic. His latest book: The Mind of the Market.

Image source and license reference

On the unattainable perfection of nature - Dr. Oren Hasson

The director of the Google development center in Tel Aviv: Mathematics has proven itself to be the best tool to solve technological problems