Maps lie more than one usually thinks

I performed the following experiment with students of mathematics. I showed them a map of Russia on google and took a point very far to the east (Uelen, a village in the Chukotsky District next to the Bering Sea) and a point very far to the west (Venekyulya, a region in the Leningrad Oblast, at the border with Estonia). The distance between Uelen and Venekyulya is, roughly, the largest distance between two points in Russia, which is about 6000 km. I asked the students to draw a path between Uelen and Venekyulya whose length is 6000 km. Some drew the path P1 shown below which is a straight line between Uelen and Venekyulya on the google map. Others, realizing that the map is a projection of a sphere, drew path P2, slightly curved upwards.

When I showed them the actual path (see below), they were all surprised. They thought it was wrong. How can it be that the "straight line path" is so much curved upwards? Well, that's because the distortion of the map increases very rapidly when we move away from the equator.

If I had shown them the actual map, on a sphere, then they would have known what to do: they would have drawn an arc between Uelen and Venekyulya that is part of the unique great circle between them, that is, the circle centered at the Earth's center and containing Uelen and Venekyulya. This arc almost (but not quite) passes from the North Pole. To see this, we need to look at the Earth downwards from the North Pole. The picture then becomes clear and the apparent contradiction is resolved.

(Credits for this image go to https://www.jasondavies.com/maps/rotate/)

The moral of this is that we should never believe what we see. (In fact, we should never believe in anything.) Only when we have further evidence, provided by experiment, measurements, or mathematical proof should we "believe" what we see. But then the verb "believe" becomes irrelevant; at this point, we know, we do not believe. We may believe something, temporarily, until further evidence, or we may believe something because someone else we trust has done the work for us. But we should never believe something because our eyes saw it, or because a teacher once told us, or because the government or administration says so, or because a religious, for example, book writes.

One thing that bothers me with some students (and some teachers) of mathematics is that they may be comfortable with the geometry of a 5-dimensional hyperbolic space because they may have seen it in class, passed an exam on it, or doing research on it, but may be uncomfortable with down-to-Earth [sic] geometry, including knowing 2-3 proofs of the Pythagorean theorem. O tempora o mores!

Two videos, two murderers

In the first one, a soldier describes how he murdered innocent people and how he regrets it.
In the second one, a police officer is seeing murdering a guy on the street.

In both cases, the murderers acted because they had been trained to be so, and had been indoctrinated in believing that their country was behind them and supporting them.

There was no murder conviction in either case precisely because the murderers had been taught to never think and always believe in those who teach them: any conviction would necessarily require conviction of those who instilled in the murderers' minds the belief that they are allowed to kill.

In both cases, the murderers had been stripped off their faculty of reasoning.
This is why belief is such a stupid and irresponsible thing.
The sleep of reason begets monsters.

Faith is irrational

In my previous posting I discussed any religion's Achilles heel. That is, belief. And I argued that without belief any religion falls into pieces. All religions demand belief. And some demand it so vehemently that any follower must feel fear: the fear that he or she will be punished (by the mullahs, the priests, the devils, the spirits...) if he or she does not confess belief.

Belief in belief has become a "virtue". Religion has succeeded in not only demanding belief but also in elevating the concept of belief into nobility. Even non-religious people are supposed to respect those who believe. Belief in belief has become a de facto concept. And we are not supposed to question it.

I watched (on youtube) a great debate on the question of  "does science refute god" which took place last August, under the auspices of an organization called intelligence-squared. The party supporting the proposition consisted of Lawrence Krauss and Michael Shermer and those against were Dinesh D'Souza and Ian Hutchinson (an MIT engineer). Krauss and Shermer spoke based on logical arguments. The other two appeared reasonable at times but could not escape the fact that they are both supporters of a particular religion (and, of course, this immediately weakens any kind of arguments they may have). I had never heard D'Souza before but he appeared to have nothing novel to say. In particular, I was totally taken aback when he reached the point to defend faith. He said: "faith is rational". I found that amazing. He gave an example. He said that if 95% people in a village believe that there is a guy called Bill (but have never met him) and 5% don't then we must accept their opinion. Same is with god, he implied. Krauss (or Shermer--I can't remember) replied that there is a subtle point: we know that there are Bills in this world. :-) Both D'Souza and Hutchinson claimed that, through religion, they seek (and find) knowledge which is not provided by science. And, by this, they meant questions like "what is the purpose of our existence?" or "why did I make a cup of tea?" and the like. As usual, the fail to see that some questions are non-questions. Why should one even suppose that these questions are answerable. Why should there be a purpose at all? Cry as you like, there might be no purpose in your being here and no purpose in the existence of the universe. This (answers to these questions), they call "knowledge". And they claim they obtain this knowledge through religion. Not just any religion, but through the particular religion they happen to support. D'Souza was asked how come he doesn't see that religion is so much connected to someone's background/location. He replied that he grew up in India where most people are Hindu, Jain, Muslim, and Christianity is a minority. He didn't understand the question: even if he himself chose an uncommon (for his milieu) religion, the fact is that there is a very-very strong correlation between one's religion and one's place of birth. Besides, I checked it on wikipedia and saw that he was raised in a Catholic family (kind of obvious from his surname, a remnant of Portuguese colonialism).

Faith is rational, they said, and this is something I've never heard before from, supposedly, intelligent people. Hutchinson is a prof. at MIT. I don't know what D'Souza's job is. He appears to be someone who doesn't like Obama and is paid to prove that the Republican party will save the world. And then, of course, he must be a Christian. He has to be. He can't be involved in American politics without showing how much of a believer he is.

Belief/faith are not virtues. They are to be avoided. We use them, unavoidably, because we don't have infinite amount of time to check everything, but we are free to question anything. The fear to open one's mind up and ask questions (or dare express doubt) is what leads to faith. The fear of punishment also leads to faith. People in North Korea must believe in the superpowers of their leader. They must have faith. They must appear to be professing this faith publicly (else their heads will be chopped off). Tit for tat when it comes to religious faith. Or any kind of faith for that matter.

Sorry Dinesh, but faith is irrational. It makes sense only in the presence of fear or in presence of monetary incentives (being a political advocator of the Republican Party without publicly proclaiming that you are a good Christian believer will reduce your monthly salary. Guaranteed.)

The weakest point of any religion

Religion is a term which does not have a very good definition. Attempts for it can be found in the literature. For example, the father of sociology, the philosopher Emil Durkheim, defines religion as

a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden - beliefs and practices which unite into a single moral community called a Church, all those who adhere to them.

My fellow blogger Sabio spends quite a bit of blogging energy to elucidate this point. I am not a scholar of religion, neither a philosopher, and certainly not one who would devote time to come up with definitions of religion. (I don't have much time to waste.) Nevertheless, I think I know what religion is when I encounter it.

I am talking in rather vague terms because "religion" is not just a system which calls itself a religion. Example of these systems are Christianity, Islam, Judaism and Zoroastrianism (all of which have the common feature of being monotheistic). It is also a system which resembles what one traditionally would call a religion. For example, the North Korean Juche is a religion. When people blindly obey someone else's orders and have reached a point where questioning them is inconceivable, then this is religion.

One can argue, based on what almost all religions proclaim, that the main requirement of every religion is the concept of belief. Now, the word itself can have many meanings. Religious belief, however, can be characterized rather precisely. After all, all religions require belief. They require faith. Have faith and you shall be saved! Have faith in god. Tony Blair established his Blair Faith Foundation in order to teach how religion influenced his politics.

Religion requires belief. Religion requires faith.

Belief is a complex concept. It is a word that can have many meanings. But religious belief has a very important feature making it uniquely distinguishable.
Religious belief about a concept X is an increasing function of the amount of evidence against X.
That is, the more we learn about the ridiculousness about X (say X=miracles), the stronger the religious belief about X is.

But belief is the weakest point of any religion. What religious people cannot get is that any time one is asked to believe without asking, without investigating, then they are possibly being tricked into something untrue. I grew up understanding that the concept of belief is terrible. I can, of course, temporarily accept something in order to go on, but I have to question it at some point.

People believe for various reasons. One is that belief is easy. It is much easier to convince yourself to believe rather than to understand, for example. Because believing takes little work. But understanding often takes a lot of hard work. Any rational person can obviously see the flaw of the (religious) belief concept.

When I teach I ask my students not to believe me. This is tough. Students have been conditioned on the idea to believe their teacher. Again, this is because it makes life easy. A student is tuned to believe that a continuous function, which takes value 1 at the beginning of an interval and 2 at the end, must take any value in between. Sure, the teacher says so. But a proof is needed. Belief is the easy thing. Proof is, typically, the hardest.

In the recent years, a number of so-called apologists (mostly of the Christian kind, but there are Muslim too) have  sprung. See, e.g., here and here and here. There are many examples of that kind. These are people who appear to be intellectual and are typically holders of advanced degrees, awards, have done serious work on some (non-religious) subject but, at some point, go crazy and start arguing that (their particular version of) religion is explained via logic, science, empirical observation. And they have lots of supporters. Sure, people are thirsty to believe; to believe that their religion is explainable because this is what these famous, important, outstanding public "intellectuals" advocate. They become the heroes of the unthinking masses. Despite all their attempts to "scientifically prove" that belief is not the main characteristic of religion, they fail, and fail badly. Religious belief remains religious belief and none of these pseudo-intellectuals have provided a gram of evidence against it.

Jesus said to him, “Have you believed because you have seen me? Blessed are those who have not seen and yet have believed.” [John, 20:29]

God will test believers to make sure they believe and are afraid. If they fail a second test they will suffer a painful punishment: 
O you who have believed, Allah will surely test you through something of the game that your hands and spears [can] reach, that Allah may make evident those who fear Him unseen. And whoever transgresses after that - for him is a painful punishment. [Quran, Sura 5:94]