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!

George Pell: more blunders

In my previous posting I pointed out that, in the Dawkins-Pell Q&A session, George Pell thought that non-randomness is equivalent to "having a purpose". Here are some more of his blunders. He claimed that:

• Humans evolved from Neanderthals. When Dawkins pointed out to him that this is not correct, because Neanderthals are more like our cousins, Pell defended his position by saying that this cannot be true because he does not see any Neanderthals around. Then Dawkins told him they are extinct.                                                            
• Jews were not intellectually equal of the Egyptians and Persians. He also said that Jews were shepherds, stuck between great powers, and are still stuck. Here, Pell confuses the term "intellectual" and "great power". He seems to be implying that, because the Persians had a mighty empire, that automatically implies that they were the intellectuals of the day too.
• Germans [during or after WWII] suffered more than the Jews [during the Holocaust]. Pell mentioned this as a response to a question on suffering. Yes, Jews suffered, but god arranged so that Germans suffered too, he, more or less said, just as much. (He subsequently issued a statement clarifying his comments and insisting he did not intend to offend the Jewish community.)
• During holy communion, the wafer and the wine turns, literally, into the body and blood of Christ. So that whoever received holy communion actually consumes flesh and blood. I know this is a cliche among Catholics, they actually believe that, but it is funny to hear it from an "authority". His explanation for this miracle is: Jesus said so. (End of story. Quod Erat Demonstrandum.)
• Science cannot give us the reason why we are here. Correct. But he does not understand that this is a silly statement. Why should there be a reason in the first place? (See previous posting on Lennox too.) Equivalent statements are the following: Astronomy cannot give us the reason for the existence of rings of Saturn. No, George, science is not so petty to deal with this. Science will give you the process for the formation of the rings, not their teleological property which, after all, is a product of projection of human behaviour to nature.
• One of our problems is that we don't understand why suffering exists, but it is a much greater problem for atheists  to explain why there is goodness and truth and beauty. This is related to the last one.

The discussion was full of such gems. It's a video worth watching. I'll leave it at that. If you spot more blunders, let me know.

John Lennox, his aunt Matilda (and her pies), and Creationism

There are religious folk, like George Pell, who was my previous post's subject, who are decent enough to suggest (or appear to be doing so) that one cannot approach religion through science, that it is beyond it, something else, etc., although they fail to suggest what this something else is. Bill Hick, of Revelation TV is such a decent chap. He has all kinds of crazy beliefs, but he doesn't say that they are the result of a scientific process.

There are others, however, like John Lennox, Oxford Professor in Mathematics (Algebra), who are trying hard to justify religion through Science. In doing so, they use their scientific hat to appear that their arguments come straight from the centres of their prestigious scientific academic establishments. It is easy: most laymen have no idea what's going on in the Oxford Mathematics Department, neither do they know whether Lennox knows Quantum Mechanics or General Relativity. All that Lennox has to do is to pretend that his religious argument comes straight from his "academic works". People will buy that, even if he will never explicitly say so.

I have been in two talks by Lennox (one was a monologue, and the other a debate with Christopher Hitchens), both in Edinburgh. On both occasions he used the following argument, a version of the Pie Argument, as anadder calls it:

My aunt Matilda bakes a wonderful pie. I have two friends, a physicist and a chemist. I ask the chemist to analyse the pie and he tells me, very precisely, of the chemical composition of every part of it. I ask the physicist, who reveals to me all kinds of scientific facts about the pie. But then I ask both of them: "why did aunt Matilda bake the pie?" None of the two can answer the question. No matter how hard they try to analyse the pie, scientifically, they will never be able to answer the question.

(Ergo, god exists; but Lennox, being smart enough, leaves this conclusion to the audience.)

Bravo Lennox! What a wonderful argument. Even a child can come up with a better one.

Again, however, what Lennox's fallacy is, is that he is trying to attach a purpose to the baking of the pie, a purpose which is contained within the pie itself! For better analysis of this stupidity, read anadder.

Let me add that Lennox has declared himself not a creationist, not an intelligent designer. He does not, he appears to be saying, sympathize with these fundamentalists. And yet, this year, Lennox accepted the Phillip Johnson award. Philip Johnson is one of the most despicable creationists. His achievements include: he rejects evolution; he thinks that god can be explained scientifically; he is an AIDS denialist; he fires people who don't agree with him; he suffers from islamophobia; he is, in fact, one of the founders of the intelligent design movement--a creationist spin-off; he is advisor and co-founder of the discovery institute (also known as dishonesty institute); he supports teaching of creationism in public schools. More on Phillip Johnson, here.

Now, how can one reconcile (i) accepting an award that bears the name of one of the most vicious creationists and (ii) claim that you do not support creationism? I'd be really ashamed.

Cardinal Pell: "Could you explain what non-random means?"

In April 2012, the Australian TV hosted a Q&A session with Richard Dawkins and George Pell (Catholic Cardinal of Australia) as respondents. I watched the 1-hour programme on youtube. I recommend it, as an exercise to spotting a large number of rational mistakes by Pell. The most interesting misconception of Pell is that he does not understand the term "random". This is a serious mistake, because he has been all along thinking been basing his belief system on the following:

non-random =[equivalent to] having a purpose

And, therefore, that

random =[equivalent to] not having a purpose

I'll leave aside whether one can always be asking about purpose, and proceed in seeing, exactly, how the Cardinal reveals his inadequacy, clearly and wittingly. He starts by saying that religion is not science (correct) but people can use reason in religion, that they can they have, for example, to reason about the parts of science regarding evolution.The excerpt of the dialogue goes like this:

• Pell: People have to ask whether they believe that random selection is sufficient. Most evolutionary biologists don't believe in this crude fundamentalist version of random selection that you propose.
• Dawkins: I do not propose it. I strongly deny that evolution is random selection. It is non-random selection.
• P: Oh, so there's a purpose to it?
• D: No.
• P: Could you explain what non-random means?

And then Dawkins goes on to explain that, in evolution, there is random genetic variation and non-random reproduction, which is why, as time goes by, animals get better at doing what they do. Natural selection, Dawkins says, is quintessentially non-random. And then he explains the obvious: that, in hindsight, it may appear that things (a bird's wing, a human's eye) have a purpose but this is a pseudo-purpose. Darwinian evolution is non-random evolution.

Ok, so Pell has had a misunderstanding of what evolution is about. But this is not his most serious mistake. After all, he claims, that a Catholic may believe in evolution if he or she likes. (Notice how he uses the verb "believe", as if there is a choice to believe or not a scientific fact; for instance, I have no choice in believing that gravitational force varies in inverse proportion of the square of the distance between two bodies, because it is so--period; whether I like it or not.)

His most serious mistake, which can (and I'm surely does) affect all his belief system is that he thinks that non-random is equivalent to having a purpose. It is so simple to realise the falsity of this, that it is painful to have to explain it, so I will leave it as an (easy) exercise. Pell makes this mistake because he badly wants to justify his views, so badly that he alters the meaning of things. Assigning purpose to concepts (such as "randomness") and to natural things (such as "the Earth") is an attempt to anthropomorphize Nature and the kind of Language we use to understand Nature. "God is created in Man's image" is what Pell's belief system is all about, and, therefore, he seems to believe that everything behaves in the same way that humans behave. The purpose found in human actions cannot be transferred to natural objects and concepts (teleology).

Not only the formula "non-random = having a purpose" is wrong because one can show that the two sides are unequal, but it is one which, simply, cannot be written down, like one cannot write down the formula "2+5 = the Moon's beauty".

A similar fallacy can be seen in John Lennox's Pie Argument, of which I'll say something next.

38':25''--39':30'' COULD YOU EXPLAIN WHAT NON-RANDOM MEANS?