Super-accurate Innumeracy

A.K. Dewdney

Between 1984 and 1991, A.K. Dewdney authored numerous articles in the section on Mathematical Games of Scientific American. He was one of the successors to Martin Gardner, most famous contributor of that section. Dewdney is also the author of an amazing book, The Planiverse (1984), which belongs to the same genre of mathematical fantasy as Edwin Abbott's Flatland, published just a century earlier.

In the previous post I offered a few examples of innumeracy taken from A.K. Dewdney’s book 200% of Nothing. In this book, Dewdney points out, among many others, two very frequent mathematical mistakes. The first consists in giving so few digits of a number that it loses all usefulness (he calls those numbers nums, to indicate that they are not full numbers, as they are not complete). The second mistake is the opposite: giving too many digits of a number, beyond what is necessary or makes sense. He calls unnecessary digits dramadigits, as they only serve to give the particular number a more dramatic look.

Let's look at an example from Dewdney's book:

Innumeracy

Douglas Hofstadter

Douglas Hofstadter, the author of the book Gödel, Escher, Bach, an Eternal Golden Braid, coined the word innumeracy, by analogy to the word illiteracy, to mean the lack of mathematical knowledge affecting a large part of the population.

Let's look at an example of innumeracy proposed by A.K. Dewdney in his book 200% of Nothing:

A man finds a $5 bill, puts it in his pocket and thinks: "As I have a $10 bill in my other pocket, I just won 50%." When he arrives at home, he discovers that he has lost the $5 note he had found. He then thinks: “As I had $15 and have lost $5, I have suffered a 33% loss. As previously I had won 50%, overall I have won 17%.”

Towards a reasonable use of COVID vaccines

There is a lot of controversy regarding the use of vaccines against COVID-19. Although they are very varied, the reactions to this problem can be classified into three large groups:

1.     Some (especially governments) are frankly in favor of everyone getting vaccinated.

2.     Others (usually specific individuals) openly oppose vaccination, either because they deny that the disease exists (deniers), or because they doubt the usefulness of vaccines, or because they consider them dangerous.

3.     A third group is in favor of the conscious and reasoned use of vaccines, but opposes compulsory vaccination, considering that such compulsion would be a violation of individual freedom and human rights.

The hijacking of the Big Bang

The Big Bang theory was invented in 1931 by the Belgian priest Georges Lemaître, through the backward application in time of the Hubble-Lemaître law, discovered by Lemaître in 1927 and independently by Hubble in 1929. Indeed, if most galaxies are moving away from one another, because of the expansion of the space separating them, billions of years ago they must have been much closer, and at the limit all the visible universe would have shrunk to a point. We believe today that this happened about 13.8 billion years ago.

In 1948, George Gamow, Ralph Alpher and Robert Herman made two predictions that should be fulfilled if the Big Bang theory were true: the mass of the universe should consist of about 75% hydrogen and 25% helium; and there should exist a cosmic background radiation with a temperature of about 5º Kelvin. Other cosmologists, however, took this theory as a joke, and to make fun of it they gave it the name Big Bang, which although not quite appropriate, has remained fixed, perhaps forever.

The weak anthropic principle: Are we alone in the galaxy?

Allen Telescope Array in the SETI project

In its initial formulation, the weak anthropic principle says that, although the appearance of intelligent life on a planet may be very unlikely, the Earth must meet all the conditions, since we exist. We know that the Milky Way contains about 10¹¹ stars. At least one (the sun) has a planet populated by intelligent life. It looks like the probability of this happening should be equal to or greater than 10^-11. Note that the weak anthropic principle does not say what the value of that probability might be.

Copyright and e-books

In other posts I spoke about the chaos of copyright rules and about e-books, pirated or not, that can be downloaded for free from the Internet. In this post I am going to add a few of my ideas in this regard.

• Just now, the European Union and the United States apply the rule that copyright lasts up to 70 years after the author's death, or almost three generations. As authors often die now at quite advanced ages, that means that the rights to their books last until the fourth or fifth generation after their own. I doubt that great-great-grandchildren and their children should continue to collect royalties for what their remote ancestor did?
• It is clear that the objective of such long duration is not to benefit authors, but publishers, many of which are very powerful, dominate mass media, and use them to pressure governments to extend the duration of copyright to their benefit, up to about a century. I think this is an abuse; governments should not have given in to these pressures. In my opinion copyright should disappear, at the latest, 25 years after the death of the author.

The best years of our lives

I have taken the title of this post from a famous film directed by William Wyler and released in 1946 (the year I was born). But in this post I am not going to deal with films, but with the different types of years.

Like the day, the year is a natural cycle, defined by the movement of the Earth around the sun. Unlike the day, which varies continuously and for which we must use the average duration, the solar year is fairly constant, as two different years are almost the same duration, although not exactly, so the concept of mean solar year is also used.

As with the hours, days and months, there are also several types of years, which differ slightly from each other, depending on the reference point considered (see the attached table).