The Dunning-Kruger effect

He who knows, and knows that he knows, is wise. Follow him.

He who knows, and knows not that he knows, is asleep. Wake him.

He who knows not, and knows that he knows not, is ignorant. Teach him.

He who knows not, and knows not that he knows not, is a fool. Shun him.

This anonymous text is well known. It is generally presented as an Arab or Persian proverb, sometimes as a Chinese proverb, and is even mistakenly attributed to Confucius, as what is written in Analects 17:3 is different. The Dunning-Kruger effect, which refers to a study published in 1999 by these two authors in a journal of the American Psychological Association, could be considered as an experimental study on the first and last lines of the proverb.

To identify the effect that bears their name, Dunning and Kruger conducted and analyzed, with psychology students, a set of tests related to intellectual and social activities in fields such as humor, grammar and logic. They then asked the participants to self-evaluate, by answering the following three questions:

The problem of no best world

The Auschwitz concentration camp

In 1993, William Rowe proposed an atheistic philosophical argument to prove that God does not exist. Although based on the problem of evil (like so many other atheistic arguments), it takes a somewhat different turn. For this reason it has been given a name, as in the title of this post. The argument can be summed up like this:

If God exists and has created the universe, he must have created the best of all possible worlds, from the moral point of view. But given a universe, it is always possible to devise a better world, which means that the best of all possible worlds does not exist. Furthermore, our universe contains a lot of evil and is far from being one of the best. Therefore God does not exist.

It is curious that, in response to this argument, some philosophers who are believers (such as Klaas Kraay and others) have tried to refute it using the theories of the multiverse, which were originally devised by atheistic thinkers to deal with the fine-tuning problem. According to these philosophers, the problem of no best world would be solved if God had created, not a universe, but a multiverse containing all the best possible worlds, perhaps in an infinite number. I don’t think this attempt has much future. It is easy to foresee that the same argument that applies to the universe can also be applied to the multiverse, so the problem would not have been solved, it would only have been moved to a higher level.

In my opinion, the problem of no best world is poorly posed, because (as is usual with atheistic arguments) it contains a logical fallacy: the straw man; and forgets a very important question: original sin. Let's look first at the straw man fallacy, which in this case should perhaps be called the straw god fallacy. What kind of god does Rowe's problem envision?

Rowe's god is not free. If he creates, he must create the best of all possible worlds. This god is totally determined by human reason.

Materialistic atheism is so obsessed with saving determinism that when they try to formulate an idea about God, in whom they don't believe, they can't escape their obsession and imagine him as a deterministic god, unable to act freely. But is that the God of the Christians?

The God of Christianity is completely different. The main thing is that He is love, as said in the first letter of John, which implies that he is free, that he is not determined, for love without freedom has no meaning. The god Rowe envisions in his problem of no best world is not our God. If he proves that that god does not exist, we agree. In fact, Rowe's god closely approximates the god of philosophers, Plato and Aristotle. Christian philosophy concluded long ago that this god is not our God, although this approach may have provided in its time a rational approximation to monotheism.

The second difficulty with Rowe's argument is more subtle. How can we compare worlds, to find whether one is better than another? There must be some criterion. Rowe seems to think that this criterion is given by the amount of moral evil in each world. But this criterion is very dangerous. It could lead us to the conclusion that the best of all possible worlds is one where life does not exist, an empty universe, with no moral evil at all. What could move God to create such universe?

In fact, if things are pushed to the extreme in this way, it could be argued that the best of all possible worlds is the world that does not exist. If God is a Perfect Being, God alone is more perfect than God plus a created universe that by definition must be imperfect.

Mark Twain

If God wanted to create a universe, it seems logical to think that He would choose one similar to ours, where intelligent beings can exist, image of God, capable of loving and being loved. Those intelligent beings should be free, because what interest could God have in creating a universe of automata? Once this is admitted, it is inevitable that any created universe that we can imagine will contain moral evil, for a free being can decide to do evil rather than good. That is what I meant when I said that in posing his problem Rowe has forgotten original sin. If we consider what I have said, God is not to blame for the moral evil in the universe, as implicitly implied by Rowe: we are. As usual, Rowe is looking for a scapegoat, and as usual, he finds it in God, according to Mark Twain's famous phrase:

There are many scapegoats for our sins, but the most popular is Providence. (Notebook, 1898).

In fact, the problem of no best world is ill-posed, since it is impossible to compare different imaginary worlds and classify them according to the moral evil they contain, if that evil comes from the freedom of created individuals, as an inescapable consequence of the fact of they are free. That is why I don’t think it appropriate to try to solve a problem that does not really exist, by resorting to multiverse theories that have probably nothing to do with reality.

The same post in Spanish
Thematic Thread on Science, Faith and Atheism: Previous Next

Manuel Alfonseca

Badly designed polls and surveys

A social network specialized in young people performed a few years ago a poll among its members to find out their habits of connection. By the way they asked a few questions to check their knowledge:

·         Do you know how much is a gigabyte of data? 63% answered yes.

·         Do you know how many photos fit in one gigabyte? It should be understood that the question refers to photos taken with a mobile phone, for otherwise the question does not make sense, as the answer depends on the dimensions and resolution of the photos. The authors of the poll assumed that a typical photo takes 70 kilobytes, which means that 14,900 of these photos would fit in a gigabyte (1,048,576 kilobytes). The correct answer they expected was “around 10,000.” (The other options offered were “around 5,000” “around 2,500” and “around 1,000”). Only 10% of those who took the poll gave the expected answer.

·         Do you know how many YouTube videos fit in a gigabyte? This question is clearly absurd, since the answer depends on the size of a YouTube video, which depends on its duration. The researchers estimated that an average YouTube video contains between 1.5 and 3 megabytes, so they expected “around 500” as the correct answer. (The other options were “around 200” “around 100” and “around 50”). Only 7% of respondents gave the expected answer.

From the previous answers, the pollsters concluded that young people do not know the size of a gigabyte of data, although they think they do. Apart from the fact that the survey is poorly designed, as the questions are ambiguous, to understand the results we need to know the answer to the following question:

·         Were the respondents told that a typical photo in the second question takes 70 kB, and that a typical video in the third question take about 2 MB? If they weren’t told, they were not given enough information to answer the questions, and the conclusion of the survey should be: young people don’t know the size of a typical photo or an average YouTube video. If they were given that information, the conclusion should be completely different: young people don’t know how to divide. In both cases, the conclusion drawn by the pollsters is wrong.

In fact, the correct response to such poorly designed questions should have been: I don't know. But today almost nobody gives that answer, because most of us believe that we know everything.


Thematic Thread on Statistics: Previous Next

Manuel Alfonseca

Scientific facts, historical facts

The possibility of repeating an experiment is one of the fundamental principles of the scientific method. No discovery is considered final until it has been confirmed by an independent team or researcher. If this happens, it becomes part of the scientific heritage. It follows, therefore, that a fact can only be considered scientific if it can be reproduced.

Historical facts are treated in a very different way. Documents describing the event are sought to confirm that it actually happened. Those documents are analyzed to estimate their degree of credibility. A historical fact will be more credible as a function of the number of independent documents that tell about it. The assassination of Julius Caesar is a well-documented historical fact, but it is not scientific, as it cannot be reproduced.

The origin of life is an event that most likely happened only once in Earth's history. It is impossible to repeat it, so as to study how it happened, therefore it is not a scientific fact. It is a historical fact.

What would be the documents, in the case of the origin of life? Fossil remains. But it is practically impossible to find them. Therefore, the origin of life will most likely be an insoluble problem forever.

But what if one day we make synthetic life in the laboratory? Wouldn’t we know then how the origin of life took place? Well no, for we wouldn’t be sure that the way in which we had made synthetic life were the same as when it appeared spontaneously, a few hundred million years after the origin of the Earth.

The same post in Spanish

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Manuel Alfonseca

What is a good scientific popularization?

Isaac Asimov

This news was published on November 20, 2007 in the Spanish major newspaper ABC:

Jugene, the most powerful and ecological civilian computer in the world, is German. [In the] Rhinelandic town of Jülich [was installed] Jugene (Jülicher Blue Gene), whose 167,000 million basic operations (teraflops) per second make it the world's first computer for civilian use...

Actually, the most powerful computers at the time could run at a few hundred teraflops. This news exaggerated the speed of the computer by nine orders of magnitude. This error has not been corrected. It’s still in the web.

Heard on a Radio broadcast on May 30, 2008: Fishermen complain about the rising price of diesel. Five years ago it cost them 320% less. In other words, five years ago they were paid to fill the tank.

Let's look at another example of a wrong headline published on 2/18/2020. The headline says: New green technology generates electricity "out of thin air." The text clarifies that it is generated from the humidity of the air acting on a protein.

These errors, so frequent in the media (I could contribute many more), have led me to formulate the following golden rule of scientific popularization:

Any statement you assert must be correct and contrastable.

Everything one says must be carefully checked to ensure that it is not a mistake, hasty or misrepresented news, or in the worst case, fake news.

Another typical error of scientific popularization in the media is showing as already done news that are really nothing but predictions about the future. This usually happens in headlines, which are usually reduced to the minimum, while keeping maximum impact. For instance, in a recent news published on 2/12/2020, the headline is: Mars was also beaten and for a long time. The text, however, is much less conclusive. What the headline gives as certain, becomes just possible: The red planet could have formed in a longer time scale than previously thought.

Statistics are prone to many manipulations, sometimes with unexpected consequences:

In 1995, one study showed that the contraceptive pill increases the risk of thrombus embolism by 100%. The press published it with great headlines. Thousands of women stopped taking the pill. It is estimated that, as a result, 10,000 more abortions took place, only in Great Britain.

What had really happened? What did that study discover?

Risk of thrombo-embolism in women who do not take the pill: 1 in 14,000. Risk of thrombus embolism in women taking the pill: 2 in 14,000.

In this case, the news was not incorrect. What was wrong was the way of making it public. It’s true, the risk increased by 100% (from 0.00007 to 0.00014). But expressed in that way, it could cause a panic, and it did.

I have given more examples in two old posts in this blog: this one and this one.

This is a list of 24 famous popularizers:

Michael Faraday

Galileo Galilei, Michael Faraday, Jean Martin Charcot, Camille Flammarion, Santiago Ramón y Cajal, Josep Comas and Solà, Gregorio Marañón, George Gamow, Willy Ley, Isaac Asimov, Arthur C. Clarke, Konrad Lorenz, Stephen Jay Gould, Martin Gardner, Félix Rodríguez de la Fuente, Douglas Hofstadter, Ian Stewart, Raymond Smullyan, Steven Weinberg, Richard Feynman, Carl Sagan, Stephen Hawking, Roger Penrose and Paul Davies.

Santiago Ramón y Cajal

Most of them were scientists, distributed among the following fields: 3 mathematicians; 12 physicists, chemists and astronomers; 3 biologists; 4 doctors in medicine; and an engineer. The exception is Martin Gardner, who graduated in philosophy, although he later specialized in philosophy of mathematics. Some of them worked on several disciplines, or kept up to date with them, at least from the informative point of view.

Many of the popularizers mentioned above also addressed the other way of popularizing science: by means of fiction. Some of the names indicated are also famous as authors of science fiction novels, or just fiction, with some scientific stroke: Asimov, Clarke, Gamow, Sagan, Davies, Ramón y Cajal, and Marañón wrote novels, some of which are considered among the best in the genre.

Are popularizers born or made? Surely both things at once. The best definition of a popularizer was given by Willy Ley, when one of his teachers asked the students to write a composition developing the following question: which profession do I want to practice when I’ll be grown up, and why? Willy Ley replied: I want to be an explorer. The teacher did not like the answer, and said there was nothing left to explore. Obviously, the teacher was wrong.

The same post in Spanish
Thematic Thread on Popularization of Science: Previous Next

Manuel Alfonseca
Happy summer holidays. See you by mid-August

Proposals for a reform of the calendar

As we saw in the previous post in these threads, the Gregorian calendar is practically perfect in terms of the duration of the year, since its error is about three days every ten thousand years, so we won’t have to worry about introducing new corrections until about the year 3500.

However, the calendar also affects the distribution of the year in months, weeks and days; and there, our calendar has some drawbacks: first, the months have variable durations; second, the week and the year do not keep pace: an ordinary year of 365 days contains 52 weeks and one day; a leap year, 52 weeks and two days. Therefore, the position in the week of every day of the month varies from year to year. For instance, July 1st 2020 was a Wednesday; the same date in 2021 will be a Thursday; in 2022, a Friday; in 2023, a Saturday; and in 2024, a Monday. The leap is one day in normal years and two days in leap years for all days after February 29th, and in the following year for days before that date. That is the reason for the English name leap year, for the succession of the days of the week for a given date leaps in those years.

The main consequence is this: we cannot have a unique calendar, valid for every year. The cycle of the days of the week is repeated with a periodicity of 28 years (the product of the seven days of the week by the four leap year cycle), but in fact there are just fourteen different calendars: seven for normal years, seven for leap years. In addition, it’s difficult to know, without consulting a calendar, on which day of the week falls a certain date. This is annoying, especially in a world as copious in commercial and administrative activities as ours. Wouldn't it be possible to avoid it?

Modern attempts to reform the calendar go in that direction. In 1954, the UN adopted a resolution, at the proposal of the Indian Union, in which all member countries were asked to study the possibility of reaching an agreement to universally adopt a calendar reform that would affect the division of the year in months and weeks. Two proposals received the attention of the international organization. The first, the international fixed calendar, divides the year into thirteen months of 28 days, plus a supernumerary day (two, in the case of leap years), which would not occupy a place in the week. The names of the months would be the same as now, except for the additional month, called sol, which would be located between June and July. All months would be identical, for they’d cover four exact weeks, and all would start on Sunday. We would have a unique calendar, valid for every month and every year: the one in the following table. The extra day, the year end day, would be placed between Saturday, December 28th and Sunday, January 1st of the following year. The other extra day in leap years would be located between Saturday June 28th and Sunday Sun 1th. This calendar has a drawback: the thirteen months of the year don’t distribute well between the four seasons: each season would last three months and one week.

S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28

International fixed calendar

The world calendar avoids this problem by dividing the year into twelve months, three per season, with the same names as the current months. The three months of each quarter would last, respectively, thirty-one, thirty, and thirty days. Each quarter would consist of thirteen weeks (ninety-one days) and would always start on a Sunday. In this case, the quarter calendar in the following table would apply to all quarters and all years. The first month of the table would apply to January, April, July and October. The second, to February, May, August and November. The third, to March, June, September and December. The additional day that would complete the 365 of the ordinary years, the world day, would be placed between Saturday, December 30th and Sunday, January 1st of the following year. The extra day of leap years would be placed between Saturday June 30th and Sunday July 1st.

The main difficulty to reach an agreement for a reform of the calendar has a religious origin: Jews, Adventists and Seventh-day Baptists oppose breaking the strict succession of the days of the week with the insertion of extra days, which would affect the interval between two consecutive Sabbaths, for them untouchable. The Catholic Church and many Protestant churches, on the other hand, don’t seem to have a problem to accept the change. Since these proposals were made, 66 years ago, nothing has been done. Change does not appear to be imminent.

D	L	M	X	J	V	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31

D	L	M	X	J	V	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30

D	L	M	X	J	V	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30

World calendar

The same post in Spanish

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Manuel Alfonseca

Is there a fifth force in Nature?

The standard model of particle physics recognizes the existence of four fundamental forces (their correct name is interactions):

• Gravitation: Newton called thus the force of attraction between any two masses at a distance. For Einstein, according to General Relativity, gravitation is the curvature of space as a consequence of the presence of a mass, which affects the movement of nearby masses. This force, which is always attractive, has an infinite range, although its effect decreases in inverse ratio of the square of the distance, and is the weakest of the four, but its effect is dominant at cosmic and planetary distances, as well as on the Earth's surface.